Question number 16. The picture shows a special die. Numbers on opposite faces always make the same sum and the numbers that we can add C are all prime numbers. The question is which number is opposite of 14? So let's write down some equations here describing our situation. We know that 14 together with the number that's opposite of 14 on the die, we'll call that X, is equal to 35 plus Y where Y is the number on the face opposite of 35 and 18 plus Z is also equal to this quantity where Z is the number on the face opposite of 18. And we know that X, Y and Z are prime. So now staring at these equations we see that for example if X is prime but X is equal to 11, 14 plus X is equal to 25 but that has to be equal to 35 plus Y so Y is negative in that equation and that cannot happen. So only X equal to 23 works. With X equal to 23 we have 14 plus 23 comes out to 37 and that is equal to 35 plus 2. So Y has to be equal to 2. If Y is equal to 2 then what happens? Then we have 37 equal to 18 plus Z and also equal to 14 plus X. That tells us already as we have discovered that X has to be equal to 23 and we also know that Z in that case has to be equal to 37 minus 18 which gives us exactly 19. All of those are prime numbers as required by the problem and so now we are sure that our solution here the number opposite of 14 that's the value of X that is 23 and so the answer here is E.

special die

opposite faces

prime sum

number 14

opposite 23