A small number of standard dice were thrown. The total of the spots on the tops was a perfect square. Then the digits that represent each of the top numbers were placed in a row in increasing order to spell out a rather large number (a given digit may appear more than once, as in 12224).

The same thing was repeated with twice as many dice and again the total number of pips was a perfect square and a number formed by using the digits that represent the pips in ascending order was the square of the first number formed that way.

What were the two numbers formed by the digits representing the pips (the first number and its square)?

A so called small number of dice is more than 6?

There are only a few numbers that can be formed with 6 or fewer digits from 3 to 6 whose digits sum to a square.

4
36
45
333
466
556
3346
3355
3445
4444
33334 whose square is 1111155556 but these sum to 31 not a square.
34666
35566
44566
45556
55555
333466
333556
334456
334555
344446
344455
444445
666666

Unless I missed one Id have to go to 7 digit numbers and my calculator isn't much help to see the 14 digit squares.

Posted by Jer on 2009-03-27 13:18:45