Place 4 points in a plane so, that the 6 point-to-point distances will be integers and at least 5 of them will be odd.
We construct this configuration:
P
Q R
S
where, PR = 3, RS = 7, SQ = 7, QP = 5, PS = 8, QR =7
Triangle QSR is equilateral with:
< QSR = < SRQ = < RQS = 60 degrees
Also,
< QPR = 120 degrees
< SPR = 60 degrees
< QPS = 60 degrees
Therefore, precisely 5 of the distances PR, RS, SQ, QP and QR are odd and the remaining distance PS is even.
Edited on May 16, 2022, 7:02 am
Puzzle Solution
