Consider a positive integer constant n.
Ten distinct integers are placed on the vertices of a regular decagon satisfying both the following conditions:
• The product of two non adjacent integers on the decagon is a multiple of n.
• The product of any pair of adjacent integers is NOT a multiple of n.
Determine the minimum value of n.
I agree with the other solutions.
This way numbering of the vertices applies to any regular m-gon. Where m=10 for this problem.
(m=2 and m=3 are trivial, just use odd numbers for the vertices and n=2)
m=4 also has a smaller minimum than 2*3*5*7=210
If the vertices are numbered 4,6,9,6 then n=36 will suffice.
(sort of the powers of primes idea H M alluded to.)
For m=5, I couldn't figure out how to beat their method.
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Posted by Jer
on 2023-04-25 16:03:20 |
smaller polygons
