A number pyramid is created such that the number in the pink triangle is equal to the sum of pairwise products of the 3 neighboring numbers in yellow triangles. For instance, in the left pyramid above, .
The right pyramid has number on top and in the remaining 5 yellow triangles.
If each of in the pink triangles is a composite number, compute .
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There are only 20 cases if we choose 3 numbers from 1,3,4,5,7,9.Only 7 cases produces composite numbers. ( 1 , 3 , 9 ) → 3 9 ( 1 , 4 , 7 ) → 3 9 ( 1 , 4 , 9 ) → 4 9 ( 3 , 4 , 9 ) → 7 5 ( 3 , 5 , 9 ) → 8 7 ( 3 , 7 , 9 ) → 1 1 1 ( 5 , 7 , 9 ) → 1 4 3 Notice the triple ( 1 , 7 , a ) .Only a = 4 fits,so 1 and 7 is on the second row.Let 1 be on the left,and 7 on the right.
Notice the triple ( 5 , b , c ) . 1 can't be adjacent to 5 ,so 5 must be on the bottom right corner.
Notice the bottom right triple ( 5 , 7 , d ) , d = 9 ,so the bottom middle number is 9
So it should be like this 4 1 3 9 7 3 3 9 9 1 4 3 5
3 9 + 3 9 + 1 4 3 = 2 2 1