## 30 Apr 2013

### Another Prime Number Cascade: Lower Secondary Mathematics Competition Question

This is a similar question to that posted yesterday, so the best place to start is to read that puzzle first.

However, in this case, you must fill the grid so that all ten prime numbers are different. What is the smallest possible prime that can go in the circle at the bottom of the triangle?

Just to recap the rules, you start by picking four different primes, one for each of the circles in the top row. For each circle below, take the two numbers immediately above it; let’s call them p and q. Calculate the three sums (p+q), (p+q+1) and (p+q-1). If one, or more, of these sums is also a prime number then pick one of them and insert it into the previously empty circle. Note that it is possible that none of the sums are prime, in which case your two numbers p and q are in the wrong places and you will need to change at least one of them.

The puzzle is to create a triangle filled with ten different prime numbers. Using the rules above, what is the smallest possible prime that can go in the last circle at the bottom of the triangle?

Note that yesterday’s prime cascade puzzle is almost the same, the only difference is that you are allowed to use the same prime number more than once. This makes yesterday’s problem slightly easier than today’s.