 10 basic strategies for problem solving. Let us now discuss logical reasoning. In reality, logical reasoning permeates all of the others, but it is so powerful that sometimes it is all you need to be able to solve a problem. Let us look at the following one. Consider this die. The sides that you cannot see are all prime numbers. Opposite faces always add up to the same number. What are the unseen numbers? Since 18 and 14 are even, the prime numbers that you add to them must be different, and hence must be odd. So when you add those even numbers with an odd number, you are going to get an odd number. Hence, 35 plus the number opposite to it must also be odd. Since 35 is odd, the only way to do that is to add an even number to it, and since 2 is the only even prime number, the number on the back face must be 2. Since that number must be 2, and opposite sides, the three pairs of opposite sides must add up to the same number, they must add up to 37. Hence, the number opposite to 18 will be 37 minus 18, that's 19 down here, and 37 minus 14, that is 23 will be the number that goes on that left face.