World!Of
Numbers

WON plate
70 |

[ December 27, 1999 ]
Find more smallest Squares and Cubes whose digits occur a same number of times ?
E.g. 100112 = 100220121 has exactly three zero's, three ones and three two's !
Note that the number of different digits in the decimal expansion
may differ from their required frequency.
The next table already give the solutions for frequencies 1 to 7 for the squares.
Though the numbers are definitely 'base-related' they surely display a notable beauty !

Some questions I would like to ask are for instance :
Are there always solutions possible for any frequency ?
What are the possible shortcuts one can make while programming this puzzle ?

FrequencySquare RootSquare
100
2887744
310.011100220121
431.646.1911001481404808481
516.431.563
3.180.566.996
269996262622969
10116006416044464016 is next one
6667.567.716445646655445456656
by Jeff Heleen - January 17, 2000
710.715.008.859114811414848448481881
by Jeff Heleen - January 20, 2000
8??
9??
10??

For the Cubes and higher Powers solutions
please visit my newest webpage solely dedicated to this interesting topic.
The title is Numbers whose digits occur with same frequency.

A000070 Prime Curios! Prime Puzzle
Wikipedia 70 Le Nombre 70 Numberland 70
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