Triangle numbers

Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.

Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?

Trinni rearanges numbers on a clock face so each adjacent pair add up to a triangle number... What number did she put where 6 would usually be?

Sam displays cans in 3 triangular stacks. With the same number he could make one large triangular stack or stack them all in a square based pyramid. How many cans are there how were they arranged?

Here is a collection of puzzles about Sam's shop sent in by club members. Perhaps you can make up more puzzles, find formulas or find general methods.

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

Can you find any two-digit numbers that satisfy all of these statements?

This activity creates an opportunity to explore all kinds of number-related patterns.