You just bought a box of chocolates for your sweetie. There are fifteen chocolates. Looking down at the contents, you see they are arranged in three rows of five. According to the key, the arrangement of flavours is symmetrical, so the top row is the same as the bottom row, the left column is the same as the right column, and the second columns in from both sides are the same. There are six flavours of fillings: cherry, strawberry, and raspberry (the reds) and orange, lemon, and blueberry.
Given the following clues, what is the arrangement of chocolates?
1) Lemon are not on the corner, strawberry not on the inside, and cherry not next to lemon (not counting diagonal).
2) The number of lemon plus cherry is equal to the number of raspberry plus orange.
3) There is only one blueberry chocolate.
4) Fewer than one-half of the chocolates are red flavours.
5) There are four each of two flavours, two each of three flavours, and one of the last flavour.
Submit your answer to Gene Wirchenko <firstname.lastname@example.org>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, February 21, 2018 at noon Pacific Time. I will post the answer shortly after.