perplexus.info :: Numbers : All 10 Digits

All 10 Digits (Posted on 2008-08-12)

Pat has made up a list of 5-digit perfect squares (all different) which use only the digits 0 through 4, none of them starting or ending with a zero. Each of the digits 0 through 4 is used a different number of times, those numbers of times being 5 through 9.

Mike has also chosen some 5-digit perfect squares, but using only the digits from 5 through 9. Each of his digits 5 through 9 is used a different number of times in his squares, those numbers of times being 0 through 4.

What were the eligible squares for each of Pat and Mike, based on their constituent digits? Which of them did each actually use?

Submitted by Charlie

Rating: 5.0000 (1 votes)

Solution: (Hide)

The eligible squares for Pat were:

10201 10404 12321 22201 23104 32041 33124 40401

of which he used all but 22201. This resulted in 5 3's, 6 2's, 7 4's, 8 0's and 9 1's.
For Mike, the eligible squares were:

55696 69696 97969 98596 99856

of which he used only 55696 and 97969, resulting in zero 8's, 1 7, 2 5's, 3 6's and 4 9's.
From Enigma No. 1504, by Richard England, New Scientist, 26 July 2008.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-02-18 22:09:15
computer solution (spoiler)	Daniel	2008-08-12 17:24:22
Clues	ed bottemiller	2008-08-12 12:43:39

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