Challenge Level

Five integers (whole numbers) are placed on the bottom row of this pyramid. They must satisfy the following conditions:

- No zeros or negative numbers are allowed
- The five numbers on the bottom row must add up to $20$

Each number in the upper rows of the pyramid is formed by combining the two numbers below it, according to the following rules:

- If the two numbers below are even, you add them to get the one above
- If the two numbers below are odd, you take the smaller from the larger to get the one above
- If one number is odd and one is even, you multiply the two numbers to get the one above

Try starting with $4, 6, 1, 7, 2$ on the bottom row. What do you get at the top?

You should have got $60$ at the top. You can see the completed pyramid in the Getting Started section.

**What is the largest top number you can obtain?**

**Extension:**

What is the largest top number you can obtain if zeroes are allowed?

What is the largest top number you can obtain if negative numbers are allowed?

*With thanks to Don Steward, whose ideas formed the basis of this problem.*