Problem 6: Logo Logic

This week’s puzzle is inspired by 1729 Maths School’s logo. Use the clues below to write a positive integer in each triangle.

Clues:

• Each triangle contains an integer
• Triangles ‘pointing right’ contain primes
• All the primes are distinct, and none exceeds 20
• Triangles ‘pointing left’ do not contain primes
• Each non-prime is equal to the product of the primes around it (i.e. their triangles share an edge)
• An odd number of triangles contain even numbers
• The sum of the numbers in white triangles is equal to the sum of the numbers in green triangles.