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Dicey numbers (Posted on 2009-03-27) Difficulty: 3 of 5
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)?

See The Solution Submitted by Charlie    
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A starting observation. | Comment 1 of 6
If an n digit number is squared it will not always double in length as required here.   In fact it only will if the number is at least the square root of 10 times 10 to the power of n.

In practical terms: you cant have any 1s or 2s in the first number.

This simplifies any searching.

Edited on March 27, 2009, 12:58 pm
  Posted by Jer on 2009-03-27 12:56:37

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