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| Going pandigital with P and Q (Posted on 2008-10-11) |
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Determine all possible pair(s) (P, Q) of 5-digit perfect squares, such that P and Q together contain each of the digits 0 to 9 exactly once. Neither P nor Q can contain any leading zeroes.
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Submitted by K Sengupta
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Rating: 1.6667 (3 votes)
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Solution:
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There are precisely 16 pairs of of 5-digit perfect squares (P, Q) that satisfy the given conditions, and these are:
( 15876, 23409), ( 15876, 39204), ( 20736, 51984), ( 20736, 95481), ( 23409, 15876), ( 30276, 51984),( 30276, 95481),( 38025, 47961),( 39204, 15876),( 47961, 38025),( 51984, 20736),
( 51984, 30276),( 63504, 71289),( 71289, 63504),( 95481, 20736), ( 95481, 30276).
Both Daniel and Dej Mar arrived at the same conclusion in their respective submitted solutions. Dej Mar further extends the problem by including the permissibility of leading zero, which would yield six additional pairs (P, Q) as:
( 03249, 15876), ( 04356, 71289), ( 08649, 35721), ( 15876,03249), ( 35721, 08649), ( 71289, 04356)
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