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Top-heavy Pyramids

Age 11 to 14
Challenge Level


This problem follows on from More Number Pyramids.
 

These are top-heavy pyramids. The blue one has $21$ at the apex (top) and the red one has $31$.

 

A pair of numbers are added to make the number above that pair.

In the blue top-heavy pyramid whose base is $4$, $5$ and $7$, $4 + 5 = 9$, so $9$ is placed between and above the $4$ and the $5$.
$5 + 7 = 12$ and $9 + 12 = 21$.

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is $200$.

numbers 1, 3, 4, 8, 9, 12