[ 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 ?
| Frequency | Square Root | Square |
|---|
| 1 | 0 | 0 |
| 2 | 88 | 7744 |
| 3 | 10.011 | 100220121 |
| 4 | 31.646.191 | 1001481404808481 |
| 5 | 16.431.563
3.180.566.996 | 269996262622969
10116006416044464016 is next one |
| 6 | 667.567.716 | 445646655445456656
by Jeff Heleen [ January 17, 2000 ] |
| 7 | 10.715.008.859 | 114811414848448481881
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 