The six faces of a die are marked with the numbers 1, 2, and 3 with each number occuring precisely twice.
- Four friends - Alec, Barry, Caleb, and Derek are sitting around the table so that each one is able to see only three sides of the die at a glance.
- Alec sees the number 1 and exactly two even numbers.
- Each of Barry and Caleb sees exactly three distinct numbers.
- Derek sees number 2 twice and he can't remember the third number.
What number is face down on the table?
Answer: 3
Trying the possibilities, only one emerges:
D | 1 | C
----------
2 | 2 | 3
----------
A | 1 | B
where this is a arial view with 2 on the top (at the center of the grid).
One folds along the lines to make the cube, and the viewers are in the corners.
soln
