Calendar Capers

Choose any three by three square of dates on a calendar page...

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

Top-heavy Pyramids

Stage: 3 Challenge Level:

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 $200$.