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The perfect squares from 1 through 2500 inclusive, are printed in a sequence of digits 1491625.....2500  What is the 100th digit in this sequence?

 Dec 25, 2020
 #1
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Just list them out and count to 100th one

 

1491625 ... 36 49 64 81 100 121 144 169 196 225 256 289 325 361 400 441 484 529 576 625 676 729 784 841 300 961 1024 1089 1156 1225 1296

         1369 1444 1521 1600       

 Dec 25, 2020
 #2
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1491625364964811001211441691962252562893243614004414845295766256767297848419009611024108911561225129

 

The 100th digit is 9, which comes from 36^2==1296

 Dec 25, 2020
 #3
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The perfect squares from 1 through 2500 inclusive, are printed in a sequence of digits 1491625.....2500  What is the 100th digit in this sequence?    

 

By brute force I found it to be 9,  You'd better check my figures though just to be sure. 

 

                  Squares                                      # in row      Running Total 

 

1 4 9 16 25 36 49 64 81 100                            18                   18  

121 144 169 196 225 256 289                         21                   39  

324 361 400 441 484 529 576 625                  24                   63  

676 729 784 841 900 961 1024 1089              26                   89  

1156 1225 1296                                               12                 101  

                                                                                                    

 Dec 25, 2020

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