Calculate 1 to 100 Square in few seconds

The 1 to 100 square method is a mathematical formula for finding the square of any number from 1 to 100. The formula is: (n+50)2−2500=n2+100n.

I came across a youtube lesson by Navneet Tiwari where he explained how to calculate Square of any number from 26 to 100 using two methods

  1. Base 100 , also called Karma method for numbers near 100
  2. Base 50 , also explained protector concept for numbers near 50

I wanted to know what range of these methods so I wrote a python program to test it. to my surprises , both method work on any number I tested from 200 to 1.

So in the conclusion for easy way to calculate , stick to Karma method when number is near 100 and otherwise base50 method

Adjust l and n where l is starting point for the program and n to the flooring part

For example test it with 99 to 26 as asked in Video

# main entry 
l=99 # from digit 
n=26 # to what number
# main entry 
l=99 # from digit 
n=26 # to what number
Calculate 1 to 100 Square Method | Solve in 2 Seconds | by Navneet Tiwari

Python Program which I used to test

#reference: Calculate 1 to 100 Square Method | Solve in 2 Seconds | by Navneet Tiwari
#https://www.youtube.com/watch?v=exwNectMR_g&ab_channel=Adda247

def numConcat(num1,num2):
    #convert both of them to string
    first  = num1
    second = num2
    extraNumber = 0
    
    
    if (num2 <10): # is second number is of single degits
        #print (f"Recieved {first} and {second} ")
        first = str(num1).zfill(2)
        second = str(num2).zfill(2)     
    elif (num2 > 99):
        # last 2 digits 
        second= num2 % 100
        #print (f"     Second is {second}")
        extraNumber= (num2 - second) // 100
            #print (f"     num2 is : {num2} Second  is {second} : Extra is {extraNumber}")
        first = first + extraNumber
        #second = str(num2).zfill(2)
        #print (f"First is {first} and Second is {second} , Extra is {extraNumber}")
       
    return int("{}{}".format(first, str(second).zfill(2)))

# main entry
l=200 # from digit
n=1 # to what number

while n < l :
    square=l*l
    #print (f"Square of {l} is {square} ")
    lessthan100=100-l
    first2 = l - lessthan100
    last2 = lessthan100 * lessthan100
    #print(f"Karma : first 2 digits are {first2} and last 2 digits are {last2} - {first2}{last2}")
    squareByKarma = numConcat(first2,last2)
    
    lessthan50=50-l
    protector=25

    firstSegment=protector - lessthan50
    lastSegment = lessthan50 * lessthan50
    
    squareByBase50 = numConcat(firstSegment,lastSegment)
    
    if (square == squareByBase50) :
         print(" %3d - Base  50 : first segments of digits are %3d and square of last 2 digits are %3d - %5d"  % (l,firstSegment,lastSegment,squareByBase50) )
    else:
       print(f"Issue: {l} Square is {square} - 50 Base method -> First 2 digits are {firstSegment} and square of last 2 digits are {lastSegment} - {squareByBase50}")
 
     
    if (square == squareByKarma) :
        #print ("Same")
        print(" %3d - Base 100 : first segments of digits are %3d and square of last 2 digits are %3d - %5d"  % (l,first2,last2,squareByKarma) )
        #print("Number : %3d - Square: %5d - Karma method : %4d"  % (l,square,squareByKarma) )
    else:
        #print (f"Square of {l} is {square} ")
        print(f"Issue: {l} Square is {square} - Karma method -> First 2 digits are {first2} and square of last 2 digits are {last2} - {squareByKarma}")
    
    l = l - 1

Program output

200 – Base 50 : first segments of digits are 175 and square of last 2 digits are 22500 – 40000
200 – Base 100 : first segments of digits are 300 and square of last 2 digits are 10000 – 40000
199 – Base 50 : first segments of digits are 174 and square of last 2 digits are 22201 – 39601
199 – Base 100 : first segments of digits are 298 and square of last 2 digits are 9801 – 39601
198 – Base 50 : first segments of digits are 173 and square of last 2 digits are 21904 – 39204
198 – Base 100 : first segments of digits are 296 and square of last 2 digits are 9604 – 39204
197 – Base 50 : first segments of digits are 172 and square of last 2 digits are 21609 – 38809
197 – Base 100 : first segments of digits are 294 and square of last 2 digits are 9409 – 38809
196 – Base 50 : first segments of digits are 171 and square of last 2 digits are 21316 – 38416
196 – Base 100 : first segments of digits are 292 and square of last 2 digits are 9216 – 38416
195 – Base 50 : first segments of digits are 170 and square of last 2 digits are 21025 – 38025
195 – Base 100 : first segments of digits are 290 and square of last 2 digits are 9025 – 38025
194 – Base 50 : first segments of digits are 169 and square of last 2 digits are 20736 – 37636
194 – Base 100 : first segments of digits are 288 and square of last 2 digits are 8836 – 37636
193 – Base 50 : first segments of digits are 168 and square of last 2 digits are 20449 – 37249
193 – Base 100 : first segments of digits are 286 and square of last 2 digits are 8649 – 37249
192 – Base 50 : first segments of digits are 167 and square of last 2 digits are 20164 – 36864
192 – Base 100 : first segments of digits are 284 and square of last 2 digits are 8464 – 36864
191 – Base 50 : first segments of digits are 166 and square of last 2 digits are 19881 – 36481
191 – Base 100 : first segments of digits are 282 and square of last 2 digits are 8281 – 36481
190 – Base 50 : first segments of digits are 165 and square of last 2 digits are 19600 – 36100
190 – Base 100 : first segments of digits are 280 and square of last 2 digits are 8100 – 36100
189 – Base 50 : first segments of digits are 164 and square of last 2 digits are 19321 – 35721
189 – Base 100 : first segments of digits are 278 and square of last 2 digits are 7921 – 35721
188 – Base 50 : first segments of digits are 163 and square of last 2 digits are 19044 – 35344
188 – Base 100 : first segments of digits are 276 and square of last 2 digits are 7744 – 35344
187 – Base 50 : first segments of digits are 162 and square of last 2 digits are 18769 – 34969
187 – Base 100 : first segments of digits are 274 and square of last 2 digits are 7569 – 34969
186 – Base 50 : first segments of digits are 161 and square of last 2 digits are 18496 – 34596
186 – Base 100 : first segments of digits are 272 and square of last 2 digits are 7396 – 34596
185 – Base 50 : first segments of digits are 160 and square of last 2 digits are 18225 – 34225
185 – Base 100 : first segments of digits are 270 and square of last 2 digits are 7225 – 34225
184 – Base 50 : first segments of digits are 159 and square of last 2 digits are 17956 – 33856
184 – Base 100 : first segments of digits are 268 and square of last 2 digits are 7056 – 33856
183 – Base 50 : first segments of digits are 158 and square of last 2 digits are 17689 – 33489
183 – Base 100 : first segments of digits are 266 and square of last 2 digits are 6889 – 33489
182 – Base 50 : first segments of digits are 157 and square of last 2 digits are 17424 – 33124
182 – Base 100 : first segments of digits are 264 and square of last 2 digits are 6724 – 33124
181 – Base 50 : first segments of digits are 156 and square of last 2 digits are 17161 – 32761
181 – Base 100 : first segments of digits are 262 and square of last 2 digits are 6561 – 32761
180 – Base 50 : first segments of digits are 155 and square of last 2 digits are 16900 – 32400
180 – Base 100 : first segments of digits are 260 and square of last 2 digits are 6400 – 32400
179 – Base 50 : first segments of digits are 154 and square of last 2 digits are 16641 – 32041
179 – Base 100 : first segments of digits are 258 and square of last 2 digits are 6241 – 32041
178 – Base 50 : first segments of digits are 153 and square of last 2 digits are 16384 – 31684
178 – Base 100 : first segments of digits are 256 and square of last 2 digits are 6084 – 31684
177 – Base 50 : first segments of digits are 152 and square of last 2 digits are 16129 – 31329
177 – Base 100 : first segments of digits are 254 and square of last 2 digits are 5929 – 31329
176 – Base 50 : first segments of digits are 151 and square of last 2 digits are 15876 – 30976
176 – Base 100 : first segments of digits are 252 and square of last 2 digits are 5776 – 30976
175 – Base 50 : first segments of digits are 150 and square of last 2 digits are 15625 – 30625
175 – Base 100 : first segments of digits are 250 and square of last 2 digits are 5625 – 30625
174 – Base 50 : first segments of digits are 149 and square of last 2 digits are 15376 – 30276
174 – Base 100 : first segments of digits are 248 and square of last 2 digits are 5476 – 30276
173 – Base 50 : first segments of digits are 148 and square of last 2 digits are 15129 – 29929
173 – Base 100 : first segments of digits are 246 and square of last 2 digits are 5329 – 29929
172 – Base 50 : first segments of digits are 147 and square of last 2 digits are 14884 – 29584
172 – Base 100 : first segments of digits are 244 and square of last 2 digits are 5184 – 29584
171 – Base 50 : first segments of digits are 146 and square of last 2 digits are 14641 – 29241
171 – Base 100 : first segments of digits are 242 and square of last 2 digits are 5041 – 29241
170 – Base 50 : first segments of digits are 145 and square of last 2 digits are 14400 – 28900
170 – Base 100 : first segments of digits are 240 and square of last 2 digits are 4900 – 28900
169 – Base 50 : first segments of digits are 144 and square of last 2 digits are 14161 – 28561
169 – Base 100 : first segments of digits are 238 and square of last 2 digits are 4761 – 28561
168 – Base 50 : first segments of digits are 143 and square of last 2 digits are 13924 – 28224
168 – Base 100 : first segments of digits are 236 and square of last 2 digits are 4624 – 28224
167 – Base 50 : first segments of digits are 142 and square of last 2 digits are 13689 – 27889
167 – Base 100 : first segments of digits are 234 and square of last 2 digits are 4489 – 27889
166 – Base 50 : first segments of digits are 141 and square of last 2 digits are 13456 – 27556
166 – Base 100 : first segments of digits are 232 and square of last 2 digits are 4356 – 27556
165 – Base 50 : first segments of digits are 140 and square of last 2 digits are 13225 – 27225
165 – Base 100 : first segments of digits are 230 and square of last 2 digits are 4225 – 27225
164 – Base 50 : first segments of digits are 139 and square of last 2 digits are 12996 – 26896
164 – Base 100 : first segments of digits are 228 and square of last 2 digits are 4096 – 26896
163 – Base 50 : first segments of digits are 138 and square of last 2 digits are 12769 – 26569
163 – Base 100 : first segments of digits are 226 and square of last 2 digits are 3969 – 26569
162 – Base 50 : first segments of digits are 137 and square of last 2 digits are 12544 – 26244
162 – Base 100 : first segments of digits are 224 and square of last 2 digits are 3844 – 26244
161 – Base 50 : first segments of digits are 136 and square of last 2 digits are 12321 – 25921
161 – Base 100 : first segments of digits are 222 and square of last 2 digits are 3721 – 25921
160 – Base 50 : first segments of digits are 135 and square of last 2 digits are 12100 – 25600
160 – Base 100 : first segments of digits are 220 and square of last 2 digits are 3600 – 25600
159 – Base 50 : first segments of digits are 134 and square of last 2 digits are 11881 – 25281
159 – Base 100 : first segments of digits are 218 and square of last 2 digits are 3481 – 25281
158 – Base 50 : first segments of digits are 133 and square of last 2 digits are 11664 – 24964
158 – Base 100 : first segments of digits are 216 and square of last 2 digits are 3364 – 24964
157 – Base 50 : first segments of digits are 132 and square of last 2 digits are 11449 – 24649
157 – Base 100 : first segments of digits are 214 and square of last 2 digits are 3249 – 24649
156 – Base 50 : first segments of digits are 131 and square of last 2 digits are 11236 – 24336
156 – Base 100 : first segments of digits are 212 and square of last 2 digits are 3136 – 24336
155 – Base 50 : first segments of digits are 130 and square of last 2 digits are 11025 – 24025
155 – Base 100 : first segments of digits are 210 and square of last 2 digits are 3025 – 24025
154 – Base 50 : first segments of digits are 129 and square of last 2 digits are 10816 – 23716
154 – Base 100 : first segments of digits are 208 and square of last 2 digits are 2916 – 23716
153 – Base 50 : first segments of digits are 128 and square of last 2 digits are 10609 – 23409
153 – Base 100 : first segments of digits are 206 and square of last 2 digits are 2809 – 23409
152 – Base 50 : first segments of digits are 127 and square of last 2 digits are 10404 – 23104
152 – Base 100 : first segments of digits are 204 and square of last 2 digits are 2704 – 23104
151 – Base 50 : first segments of digits are 126 and square of last 2 digits are 10201 – 22801
151 – Base 100 : first segments of digits are 202 and square of last 2 digits are 2601 – 22801
150 – Base 50 : first segments of digits are 125 and square of last 2 digits are 10000 – 22500
150 – Base 100 : first segments of digits are 200 and square of last 2 digits are 2500 – 22500
149 – Base 50 : first segments of digits are 124 and square of last 2 digits are 9801 – 22201
149 – Base 100 : first segments of digits are 198 and square of last 2 digits are 2401 – 22201
148 – Base 50 : first segments of digits are 123 and square of last 2 digits are 9604 – 21904
148 – Base 100 : first segments of digits are 196 and square of last 2 digits are 2304 – 21904
147 – Base 50 : first segments of digits are 122 and square of last 2 digits are 9409 – 21609
147 – Base 100 : first segments of digits are 194 and square of last 2 digits are 2209 – 21609
146 – Base 50 : first segments of digits are 121 and square of last 2 digits are 9216 – 21316
146 – Base 100 : first segments of digits are 192 and square of last 2 digits are 2116 – 21316
145 – Base 50 : first segments of digits are 120 and square of last 2 digits are 9025 – 21025
145 – Base 100 : first segments of digits are 190 and square of last 2 digits are 2025 – 21025
144 – Base 50 : first segments of digits are 119 and square of last 2 digits are 8836 – 20736
144 – Base 100 : first segments of digits are 188 and square of last 2 digits are 1936 – 20736
143 – Base 50 : first segments of digits are 118 and square of last 2 digits are 8649 – 20449
143 – Base 100 : first segments of digits are 186 and square of last 2 digits are 1849 – 20449
142 – Base 50 : first segments of digits are 117 and square of last 2 digits are 8464 – 20164
142 – Base 100 : first segments of digits are 184 and square of last 2 digits are 1764 – 20164
141 – Base 50 : first segments of digits are 116 and square of last 2 digits are 8281 – 19881
141 – Base 100 : first segments of digits are 182 and square of last 2 digits are 1681 – 19881
140 – Base 50 : first segments of digits are 115 and square of last 2 digits are 8100 – 19600
140 – Base 100 : first segments of digits are 180 and square of last 2 digits are 1600 – 19600
139 – Base 50 : first segments of digits are 114 and square of last 2 digits are 7921 – 19321
139 – Base 100 : first segments of digits are 178 and square of last 2 digits are 1521 – 19321
138 – Base 50 : first segments of digits are 113 and square of last 2 digits are 7744 – 19044
138 – Base 100 : first segments of digits are 176 and square of last 2 digits are 1444 – 19044
137 – Base 50 : first segments of digits are 112 and square of last 2 digits are 7569 – 18769
137 – Base 100 : first segments of digits are 174 and square of last 2 digits are 1369 – 18769
136 – Base 50 : first segments of digits are 111 and square of last 2 digits are 7396 – 18496
136 – Base 100 : first segments of digits are 172 and square of last 2 digits are 1296 – 18496
135 – Base 50 : first segments of digits are 110 and square of last 2 digits are 7225 – 18225
135 – Base 100 : first segments of digits are 170 and square of last 2 digits are 1225 – 18225
134 – Base 50 : first segments of digits are 109 and square of last 2 digits are 7056 – 17956
134 – Base 100 : first segments of digits are 168 and square of last 2 digits are 1156 – 17956
133 – Base 50 : first segments of digits are 108 and square of last 2 digits are 6889 – 17689
133 – Base 100 : first segments of digits are 166 and square of last 2 digits are 1089 – 17689
132 – Base 50 : first segments of digits are 107 and square of last 2 digits are 6724 – 17424
132 – Base 100 : first segments of digits are 164 and square of last 2 digits are 1024 – 17424
131 – Base 50 : first segments of digits are 106 and square of last 2 digits are 6561 – 17161
131 – Base 100 : first segments of digits are 162 and square of last 2 digits are 961 – 17161
130 – Base 50 : first segments of digits are 105 and square of last 2 digits are 6400 – 16900
130 – Base 100 : first segments of digits are 160 and square of last 2 digits are 900 – 16900
129 – Base 50 : first segments of digits are 104 and square of last 2 digits are 6241 – 16641
129 – Base 100 : first segments of digits are 158 and square of last 2 digits are 841 – 16641
128 – Base 50 : first segments of digits are 103 and square of last 2 digits are 6084 – 16384
128 – Base 100 : first segments of digits are 156 and square of last 2 digits are 784 – 16384
127 – Base 50 : first segments of digits are 102 and square of last 2 digits are 5929 – 16129
127 – Base 100 : first segments of digits are 154 and square of last 2 digits are 729 – 16129
126 – Base 50 : first segments of digits are 101 and square of last 2 digits are 5776 – 15876
126 – Base 100 : first segments of digits are 152 and square of last 2 digits are 676 – 15876
125 – Base 50 : first segments of digits are 100 and square of last 2 digits are 5625 – 15625
125 – Base 100 : first segments of digits are 150 and square of last 2 digits are 625 – 15625
124 – Base 50 : first segments of digits are 99 and square of last 2 digits are 5476 – 15376
124 – Base 100 : first segments of digits are 148 and square of last 2 digits are 576 – 15376
123 – Base 50 : first segments of digits are 98 and square of last 2 digits are 5329 – 15129
123 – Base 100 : first segments of digits are 146 and square of last 2 digits are 529 – 15129
122 – Base 50 : first segments of digits are 97 and square of last 2 digits are 5184 – 14884
122 – Base 100 : first segments of digits are 144 and square of last 2 digits are 484 – 14884
121 – Base 50 : first segments of digits are 96 and square of last 2 digits are 5041 – 14641
121 – Base 100 : first segments of digits are 142 and square of last 2 digits are 441 – 14641
120 – Base 50 : first segments of digits are 95 and square of last 2 digits are 4900 – 14400
120 – Base 100 : first segments of digits are 140 and square of last 2 digits are 400 – 14400
119 – Base 50 : first segments of digits are 94 and square of last 2 digits are 4761 – 14161
119 – Base 100 : first segments of digits are 138 and square of last 2 digits are 361 – 14161
118 – Base 50 : first segments of digits are 93 and square of last 2 digits are 4624 – 13924
118 – Base 100 : first segments of digits are 136 and square of last 2 digits are 324 – 13924
117 – Base 50 : first segments of digits are 92 and square of last 2 digits are 4489 – 13689
117 – Base 100 : first segments of digits are 134 and square of last 2 digits are 289 – 13689
116 – Base 50 : first segments of digits are 91 and square of last 2 digits are 4356 – 13456
116 – Base 100 : first segments of digits are 132 and square of last 2 digits are 256 – 13456
115 – Base 50 : first segments of digits are 90 and square of last 2 digits are 4225 – 13225
115 – Base 100 : first segments of digits are 130 and square of last 2 digits are 225 – 13225
114 – Base 50 : first segments of digits are 89 and square of last 2 digits are 4096 – 12996
114 – Base 100 : first segments of digits are 128 and square of last 2 digits are 196 – 12996
113 – Base 50 : first segments of digits are 88 and square of last 2 digits are 3969 – 12769
113 – Base 100 : first segments of digits are 126 and square of last 2 digits are 169 – 12769
112 – Base 50 : first segments of digits are 87 and square of last 2 digits are 3844 – 12544
112 – Base 100 : first segments of digits are 124 and square of last 2 digits are 144 – 12544
111 – Base 50 : first segments of digits are 86 and square of last 2 digits are 3721 – 12321
111 – Base 100 : first segments of digits are 122 and square of last 2 digits are 121 – 12321
110 – Base 50 : first segments of digits are 85 and square of last 2 digits are 3600 – 12100
110 – Base 100 : first segments of digits are 120 and square of last 2 digits are 100 – 12100
109 – Base 50 : first segments of digits are 84 and square of last 2 digits are 3481 – 11881
109 – Base 100 : first segments of digits are 118 and square of last 2 digits are 81 – 11881
108 – Base 50 : first segments of digits are 83 and square of last 2 digits are 3364 – 11664
108 – Base 100 : first segments of digits are 116 and square of last 2 digits are 64 – 11664
107 – Base 50 : first segments of digits are 82 and square of last 2 digits are 3249 – 11449
107 – Base 100 : first segments of digits are 114 and square of last 2 digits are 49 – 11449
106 – Base 50 : first segments of digits are 81 and square of last 2 digits are 3136 – 11236
106 – Base 100 : first segments of digits are 112 and square of last 2 digits are 36 – 11236
105 – Base 50 : first segments of digits are 80 and square of last 2 digits are 3025 – 11025
105 – Base 100 : first segments of digits are 110 and square of last 2 digits are 25 – 11025
104 – Base 50 : first segments of digits are 79 and square of last 2 digits are 2916 – 10816
104 – Base 100 : first segments of digits are 108 and square of last 2 digits are 16 – 10816
103 – Base 50 : first segments of digits are 78 and square of last 2 digits are 2809 – 10609
103 – Base 100 : first segments of digits are 106 and square of last 2 digits are 9 – 10609
102 – Base 50 : first segments of digits are 77 and square of last 2 digits are 2704 – 10404
102 – Base 100 : first segments of digits are 104 and square of last 2 digits are 4 – 10404
101 – Base 50 : first segments of digits are 76 and square of last 2 digits are 2601 – 10201
101 – Base 100 : first segments of digits are 102 and square of last 2 digits are 1 – 10201
100 – Base 50 : first segments of digits are 75 and square of last 2 digits are 2500 – 10000
100 – Base 100 : first segments of digits are 100 and square of last 2 digits are 0 – 10000
99 – Base 50 : first segments of digits are 74 and square of last 2 digits are 2401 – 9801
99 – Base 100 : first segments of digits are 98 and square of last 2 digits are 1 – 9801
98 – Base 50 : first segments of digits are 73 and square of last 2 digits are 2304 – 9604
98 – Base 100 : first segments of digits are 96 and square of last 2 digits are 4 – 9604
97 – Base 50 : first segments of digits are 72 and square of last 2 digits are 2209 – 9409
97 – Base 100 : first segments of digits are 94 and square of last 2 digits are 9 – 9409
96 – Base 50 : first segments of digits are 71 and square of last 2 digits are 2116 – 9216
96 – Base 100 : first segments of digits are 92 and square of last 2 digits are 16 – 9216
95 – Base 50 : first segments of digits are 70 and square of last 2 digits are 2025 – 9025
95 – Base 100 : first segments of digits are 90 and square of last 2 digits are 25 – 9025
94 – Base 50 : first segments of digits are 69 and square of last 2 digits are 1936 – 8836
94 – Base 100 : first segments of digits are 88 and square of last 2 digits are 36 – 8836
93 – Base 50 : first segments of digits are 68 and square of last 2 digits are 1849 – 8649
93 – Base 100 : first segments of digits are 86 and square of last 2 digits are 49 – 8649
92 – Base 50 : first segments of digits are 67 and square of last 2 digits are 1764 – 8464
92 – Base 100 : first segments of digits are 84 and square of last 2 digits are 64 – 8464
91 – Base 50 : first segments of digits are 66 and square of last 2 digits are 1681 – 8281
91 – Base 100 : first segments of digits are 82 and square of last 2 digits are 81 – 8281
90 – Base 50 : first segments of digits are 65 and square of last 2 digits are 1600 – 8100
90 – Base 100 : first segments of digits are 80 and square of last 2 digits are 100 – 8100
89 – Base 50 : first segments of digits are 64 and square of last 2 digits are 1521 – 7921
89 – Base 100 : first segments of digits are 78 and square of last 2 digits are 121 – 7921
88 – Base 50 : first segments of digits are 63 and square of last 2 digits are 1444 – 7744
88 – Base 100 : first segments of digits are 76 and square of last 2 digits are 144 – 7744
87 – Base 50 : first segments of digits are 62 and square of last 2 digits are 1369 – 7569
87 – Base 100 : first segments of digits are 74 and square of last 2 digits are 169 – 7569
86 – Base 50 : first segments of digits are 61 and square of last 2 digits are 1296 – 7396
86 – Base 100 : first segments of digits are 72 and square of last 2 digits are 196 – 7396
85 – Base 50 : first segments of digits are 60 and square of last 2 digits are 1225 – 7225
85 – Base 100 : first segments of digits are 70 and square of last 2 digits are 225 – 7225
84 – Base 50 : first segments of digits are 59 and square of last 2 digits are 1156 – 7056
84 – Base 100 : first segments of digits are 68 and square of last 2 digits are 256 – 7056
83 – Base 50 : first segments of digits are 58 and square of last 2 digits are 1089 – 6889
83 – Base 100 : first segments of digits are 66 and square of last 2 digits are 289 – 6889
82 – Base 50 : first segments of digits are 57 and square of last 2 digits are 1024 – 6724
82 – Base 100 : first segments of digits are 64 and square of last 2 digits are 324 – 6724
81 – Base 50 : first segments of digits are 56 and square of last 2 digits are 961 – 6561
81 – Base 100 : first segments of digits are 62 and square of last 2 digits are 361 – 6561
80 – Base 50 : first segments of digits are 55 and square of last 2 digits are 900 – 6400
80 – Base 100 : first segments of digits are 60 and square of last 2 digits are 400 – 6400
79 – Base 50 : first segments of digits are 54 and square of last 2 digits are 841 – 6241
79 – Base 100 : first segments of digits are 58 and square of last 2 digits are 441 – 6241
78 – Base 50 : first segments of digits are 53 and square of last 2 digits are 784 – 6084
78 – Base 100 : first segments of digits are 56 and square of last 2 digits are 484 – 6084
77 – Base 50 : first segments of digits are 52 and square of last 2 digits are 729 – 5929
77 – Base 100 : first segments of digits are 54 and square of last 2 digits are 529 – 5929
76 – Base 50 : first segments of digits are 51 and square of last 2 digits are 676 – 5776
76 – Base 100 : first segments of digits are 52 and square of last 2 digits are 576 – 5776
75 – Base 50 : first segments of digits are 50 and square of last 2 digits are 625 – 5625
75 – Base 100 : first segments of digits are 50 and square of last 2 digits are 625 – 5625
74 – Base 50 : first segments of digits are 49 and square of last 2 digits are 576 – 5476
74 – Base 100 : first segments of digits are 48 and square of last 2 digits are 676 – 5476
73 – Base 50 : first segments of digits are 48 and square of last 2 digits are 529 – 5329
73 – Base 100 : first segments of digits are 46 and square of last 2 digits are 729 – 5329
72 – Base 50 : first segments of digits are 47 and square of last 2 digits are 484 – 5184
72 – Base 100 : first segments of digits are 44 and square of last 2 digits are 784 – 5184
71 – Base 50 : first segments of digits are 46 and square of last 2 digits are 441 – 5041
71 – Base 100 : first segments of digits are 42 and square of last 2 digits are 841 – 5041
70 – Base 50 : first segments of digits are 45 and square of last 2 digits are 400 – 4900
70 – Base 100 : first segments of digits are 40 and square of last 2 digits are 900 – 4900
69 – Base 50 : first segments of digits are 44 and square of last 2 digits are 361 – 4761
69 – Base 100 : first segments of digits are 38 and square of last 2 digits are 961 – 4761
68 – Base 50 : first segments of digits are 43 and square of last 2 digits are 324 – 4624
68 – Base 100 : first segments of digits are 36 and square of last 2 digits are 1024 – 4624
67 – Base 50 : first segments of digits are 42 and square of last 2 digits are 289 – 4489
67 – Base 100 : first segments of digits are 34 and square of last 2 digits are 1089 – 4489
66 – Base 50 : first segments of digits are 41 and square of last 2 digits are 256 – 4356
66 – Base 100 : first segments of digits are 32 and square of last 2 digits are 1156 – 4356
65 – Base 50 : first segments of digits are 40 and square of last 2 digits are 225 – 4225
65 – Base 100 : first segments of digits are 30 and square of last 2 digits are 1225 – 4225
64 – Base 50 : first segments of digits are 39 and square of last 2 digits are 196 – 4096
64 – Base 100 : first segments of digits are 28 and square of last 2 digits are 1296 – 4096
63 – Base 50 : first segments of digits are 38 and square of last 2 digits are 169 – 3969
63 – Base 100 : first segments of digits are 26 and square of last 2 digits are 1369 – 3969
62 – Base 50 : first segments of digits are 37 and square of last 2 digits are 144 – 3844
62 – Base 100 : first segments of digits are 24 and square of last 2 digits are 1444 – 3844
61 – Base 50 : first segments of digits are 36 and square of last 2 digits are 121 – 3721
61 – Base 100 : first segments of digits are 22 and square of last 2 digits are 1521 – 3721
60 – Base 50 : first segments of digits are 35 and square of last 2 digits are 100 – 3600
60 – Base 100 : first segments of digits are 20 and square of last 2 digits are 1600 – 3600
59 – Base 50 : first segments of digits are 34 and square of last 2 digits are 81 – 3481
59 – Base 100 : first segments of digits are 18 and square of last 2 digits are 1681 – 3481
58 – Base 50 : first segments of digits are 33 and square of last 2 digits are 64 – 3364
58 – Base 100 : first segments of digits are 16 and square of last 2 digits are 1764 – 3364
57 – Base 50 : first segments of digits are 32 and square of last 2 digits are 49 – 3249
57 – Base 100 : first segments of digits are 14 and square of last 2 digits are 1849 – 3249
56 – Base 50 : first segments of digits are 31 and square of last 2 digits are 36 – 3136
56 – Base 100 : first segments of digits are 12 and square of last 2 digits are 1936 – 3136
55 – Base 50 : first segments of digits are 30 and square of last 2 digits are 25 – 3025
55 – Base 100 : first segments of digits are 10 and square of last 2 digits are 2025 – 3025
54 – Base 50 : first segments of digits are 29 and square of last 2 digits are 16 – 2916
54 – Base 100 : first segments of digits are 8 and square of last 2 digits are 2116 – 2916
53 – Base 50 : first segments of digits are 28 and square of last 2 digits are 9 – 2809
53 – Base 100 : first segments of digits are 6 and square of last 2 digits are 2209 – 2809
52 – Base 50 : first segments of digits are 27 and square of last 2 digits are 4 – 2704
52 – Base 100 : first segments of digits are 4 and square of last 2 digits are 2304 – 2704
51 – Base 50 : first segments of digits are 26 and square of last 2 digits are 1 – 2601
51 – Base 100 : first segments of digits are 2 and square of last 2 digits are 2401 – 2601
50 – Base 50 : first segments of digits are 25 and square of last 2 digits are 0 – 2500
50 – Base 100 : first segments of digits are 0 and square of last 2 digits are 2500 – 2500
49 – Base 50 : first segments of digits are 24 and square of last 2 digits are 1 – 2401
49 – Base 100 : first segments of digits are -2 and square of last 2 digits are 2601 – 2401
48 – Base 50 : first segments of digits are 23 and square of last 2 digits are 4 – 2304
48 – Base 100 : first segments of digits are -4 and square of last 2 digits are 2704 – 2304
47 – Base 50 : first segments of digits are 22 and square of last 2 digits are 9 – 2209
47 – Base 100 : first segments of digits are -6 and square of last 2 digits are 2809 – 2209
46 – Base 50 : first segments of digits are 21 and square of last 2 digits are 16 – 2116
46 – Base 100 : first segments of digits are -8 and square of last 2 digits are 2916 – 2116
45 – Base 50 : first segments of digits are 20 and square of last 2 digits are 25 – 2025
45 – Base 100 : first segments of digits are -10 and square of last 2 digits are 3025 – 2025
44 – Base 50 : first segments of digits are 19 and square of last 2 digits are 36 – 1936
44 – Base 100 : first segments of digits are -12 and square of last 2 digits are 3136 – 1936
43 – Base 50 : first segments of digits are 18 and square of last 2 digits are 49 – 1849
43 – Base 100 : first segments of digits are -14 and square of last 2 digits are 3249 – 1849
42 – Base 50 : first segments of digits are 17 and square of last 2 digits are 64 – 1764
42 – Base 100 : first segments of digits are -16 and square of last 2 digits are 3364 – 1764
41 – Base 50 : first segments of digits are 16 and square of last 2 digits are 81 – 1681
41 – Base 100 : first segments of digits are -18 and square of last 2 digits are 3481 – 1681
40 – Base 50 : first segments of digits are 15 and square of last 2 digits are 100 – 1600
40 – Base 100 : first segments of digits are -20 and square of last 2 digits are 3600 – 1600
39 – Base 50 : first segments of digits are 14 and square of last 2 digits are 121 – 1521
39 – Base 100 : first segments of digits are -22 and square of last 2 digits are 3721 – 1521
38 – Base 50 : first segments of digits are 13 and square of last 2 digits are 144 – 1444
38 – Base 100 : first segments of digits are -24 and square of last 2 digits are 3844 – 1444
37 – Base 50 : first segments of digits are 12 and square of last 2 digits are 169 – 1369
37 – Base 100 : first segments of digits are -26 and square of last 2 digits are 3969 – 1369
36 – Base 50 : first segments of digits are 11 and square of last 2 digits are 196 – 1296
36 – Base 100 : first segments of digits are -28 and square of last 2 digits are 4096 – 1296
35 – Base 50 : first segments of digits are 10 and square of last 2 digits are 225 – 1225
35 – Base 100 : first segments of digits are -30 and square of last 2 digits are 4225 – 1225
34 – Base 50 : first segments of digits are 9 and square of last 2 digits are 256 – 1156
34 – Base 100 : first segments of digits are -32 and square of last 2 digits are 4356 – 1156
33 – Base 50 : first segments of digits are 8 and square of last 2 digits are 289 – 1089
33 – Base 100 : first segments of digits are -34 and square of last 2 digits are 4489 – 1089
32 – Base 50 : first segments of digits are 7 and square of last 2 digits are 324 – 1024
32 – Base 100 : first segments of digits are -36 and square of last 2 digits are 4624 – 1024
31 – Base 50 : first segments of digits are 6 and square of last 2 digits are 361 – 961
31 – Base 100 : first segments of digits are -38 and square of last 2 digits are 4761 – 961
30 – Base 50 : first segments of digits are 5 and square of last 2 digits are 400 – 900
30 – Base 100 : first segments of digits are -40 and square of last 2 digits are 4900 – 900
29 – Base 50 : first segments of digits are 4 and square of last 2 digits are 441 – 841
29 – Base 100 : first segments of digits are -42 and square of last 2 digits are 5041 – 841
28 – Base 50 : first segments of digits are 3 and square of last 2 digits are 484 – 784
28 – Base 100 : first segments of digits are -44 and square of last 2 digits are 5184 – 784
27 – Base 50 : first segments of digits are 2 and square of last 2 digits are 529 – 729
27 – Base 100 : first segments of digits are -46 and square of last 2 digits are 5329 – 729
26 – Base 50 : first segments of digits are 1 and square of last 2 digits are 576 – 676
26 – Base 100 : first segments of digits are -48 and square of last 2 digits are 5476 – 676
25 – Base 50 : first segments of digits are 0 and square of last 2 digits are 625 – 625
25 – Base 100 : first segments of digits are -50 and square of last 2 digits are 5625 – 625
24 – Base 50 : first segments of digits are -1 and square of last 2 digits are 676 – 576
24 – Base 100 : first segments of digits are -52 and square of last 2 digits are 5776 – 576
23 – Base 50 : first segments of digits are -2 and square of last 2 digits are 729 – 529
23 – Base 100 : first segments of digits are -54 and square of last 2 digits are 5929 – 529
22 – Base 50 : first segments of digits are -3 and square of last 2 digits are 784 – 484
22 – Base 100 : first segments of digits are -56 and square of last 2 digits are 6084 – 484
21 – Base 50 : first segments of digits are -4 and square of last 2 digits are 841 – 441
21 – Base 100 : first segments of digits are -58 and square of last 2 digits are 6241 – 441
20 – Base 50 : first segments of digits are -5 and square of last 2 digits are 900 – 400
20 – Base 100 : first segments of digits are -60 and square of last 2 digits are 6400 – 400
19 – Base 50 : first segments of digits are -6 and square of last 2 digits are 961 – 361
19 – Base 100 : first segments of digits are -62 and square of last 2 digits are 6561 – 361
18 – Base 50 : first segments of digits are -7 and square of last 2 digits are 1024 – 324
18 – Base 100 : first segments of digits are -64 and square of last 2 digits are 6724 – 324
17 – Base 50 : first segments of digits are -8 and square of last 2 digits are 1089 – 289
17 – Base 100 : first segments of digits are -66 and square of last 2 digits are 6889 – 289
16 – Base 50 : first segments of digits are -9 and square of last 2 digits are 1156 – 256
16 – Base 100 : first segments of digits are -68 and square of last 2 digits are 7056 – 256
15 – Base 50 : first segments of digits are -10 and square of last 2 digits are 1225 – 225
15 – Base 100 : first segments of digits are -70 and square of last 2 digits are 7225 – 225
14 – Base 50 : first segments of digits are -11 and square of last 2 digits are 1296 – 196
14 – Base 100 : first segments of digits are -72 and square of last 2 digits are 7396 – 196
13 – Base 50 : first segments of digits are -12 and square of last 2 digits are 1369 – 169
13 – Base 100 : first segments of digits are -74 and square of last 2 digits are 7569 – 169
12 – Base 50 : first segments of digits are -13 and square of last 2 digits are 1444 – 144
12 – Base 100 : first segments of digits are -76 and square of last 2 digits are 7744 – 144
11 – Base 50 : first segments of digits are -14 and square of last 2 digits are 1521 – 121
11 – Base 100 : first segments of digits are -78 and square of last 2 digits are 7921 – 121
10 – Base 50 : first segments of digits are -15 and square of last 2 digits are 1600 – 100
10 – Base 100 : first segments of digits are -80 and square of last 2 digits are 8100 – 100
9 – Base 50 : first segments of digits are -16 and square of last 2 digits are 1681 – 81
9 – Base 100 : first segments of digits are -82 and square of last 2 digits are 8281 – 81
8 – Base 50 : first segments of digits are -17 and square of last 2 digits are 1764 – 64
8 – Base 100 : first segments of digits are -84 and square of last 2 digits are 8464 – 64
7 – Base 50 : first segments of digits are -18 and square of last 2 digits are 1849 – 49
7 – Base 100 : first segments of digits are -86 and square of last 2 digits are 8649 – 49
6 – Base 50 : first segments of digits are -19 and square of last 2 digits are 1936 – 36
6 – Base 100 : first segments of digits are -88 and square of last 2 digits are 8836 – 36
5 – Base 50 : first segments of digits are -20 and square of last 2 digits are 2025 – 25
5 – Base 100 : first segments of digits are -90 and square of last 2 digits are 9025 – 25
4 – Base 50 : first segments of digits are -21 and square of last 2 digits are 2116 – 16
4 – Base 100 : first segments of digits are -92 and square of last 2 digits are 9216 – 16
3 – Base 50 : first segments of digits are -22 and square of last 2 digits are 2209 – 9
3 – Base 100 : first segments of digits are -94 and square of last 2 digits are 9409 – 9
2 – Base 50 : first segments of digits are -23 and square of last 2 digits are 2304 – 4
2 – Base 100 : first segments of digits are -96 and square of last 2 digits are 9604 – 4

So in the conclusion for easy way to calculate , stick to Karma method when number is near 100 and otherwise Base50 method