Determine all possible quintuplets (p, q, r, s, t) of positive integers that satisfy this equation:
⌊(p+q)/3⌋2 +⌊(q+r)/3⌋2 + ⌊(r+s)/3⌋2 + ⌊(s+t)/3⌋2 = 38
*** ⌊p⌋ is the floor function. ie. the greatest integer less than or equal to p.
****** Adapted from a problem appearing at an Austrian Mathematical Olympiad in 2007.
**** Computer program assisted solutions are welcome, but a semi-analytic methodology, that is: hand calculator and p&p, is preferred.
(In reply to
re: computer solution continued by Charlie)
9 1 6 4 9
9 1 6 4 10
9 1 6 5 9
9 1 7 2 10
9 1 7 2 11
9 1 7 2 12
9 1 7 3 9
9 1 7 3 10
9 1 7 3 11
9 1 7 4 9
9 1 7 4 10
9 2 4 5 9
9 2 5 4 9
9 2 5 4 10
9 2 5 5 9
9 2 6 3 9
9 2 6 3 10
9 2 6 3 11
9 2 6 4 9
9 2 6 4 10
9 2 6 5 9
9 2 7 1 11
9 2 7 1 12
9 2 7 1 13
9 3 6 1 10
9 3 7 1 10
9 4 5 1 10
9 4 6 1 10
9 4 7 1 10
9 5 5 1 10
9 5 6 1 10
9 6 1 1 10
9 7 1 1 10
10 1 1 5 10
10 1 1 5 11
10 1 1 5 12
10 1 1 6 10
10 1 1 6 11
10 1 1 7 10
10 1 5 4 10
10 1 6 3 10
10 1 6 3 11
10 1 6 4 10
10 1 7 2 10
10 1 7 2 11
10 1 7 2 12
10 1 7 3 10
10 1 7 3 11
10 1 7 4 10
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Posted by Charlie
on 2023-08-04 12:54:51 |
re(2): computer solution continued (last part)
