I have six tiles numbered 1 to 6. Each is a different shape, (triangle, circle, square, pentagon, hexagon and octagon) and painted a different color (red, orange, blue, yellow, green and purple.)
I arranged the tiles in two rows of 3. Given that

1) The top row formed an odd number and the bottom row a prime number
2) In the bottom row the colors were in reverse alphabetical order.
3) The Blue Number 1 was between the orange tile and the Circle;
4) The Hexagon was directly above the Red triangle numbered 4.
5) One tile has a color and shape beginning with the same letter.

Can you reproduce the layout?

There is no possible way to have a sum of a 3 numbers with the number 4 included in the bottom row equal a prime number without having the top row equal an even number. It is mathematically impossible. The sum of the 6 numbers is 21 and a prime number is odd therefore leaving an even number no matter what. If there is to be an actual answer to the puzzle there is only one format to have the answer. It has to be a 2-2-2 format which depending on how you interperet the problem is still possible. If that is the case, there is more than one possibility as a solution to this problem. I will give two here. If anyone can disprove these answers based on the 5 given facts than please let me know.

1.
(5-Orange-Octagon) (2-Green-Pentagon)
(1-Blue-Square) (6-Purple-Hexagon)
(3-Yellow-Circle) (4-Red Triangle)

2.
(2-Purple-Hexagon) (3-Green-Circle)
(4-Red-Triangle) (1-Blue-Square)
(6-Yellow-Pentagon) (5-Orange-Octagon)

Posted by mike on 2007-03-06 13:59:11