Triangle numbers

problem

Human Food

Age

7 to 14

Challenge level

1 out of 3

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?
problem

Satisfying Statements

Age

11 to 14

Challenge level

1 out of 3

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

Triangular Clock

Age

11 to 14

Challenge level

1 out of 3

Trinni rearranges 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?
problem

Forgotten Number

Age

11 to 14

Challenge level

2 out of 3

I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...
problem

Triangles Within Triangles

Age

14 to 16

Challenge level

1 out of 3

Can you find a rule which connects consecutive triangular numbers?
problem

Triangles Within Squares

Age

14 to 16

Challenge level

2 out of 3

Can you find a rule which relates triangular numbers to square numbers?
problem

Series Sums

Age

14 to 16

Challenge level

3 out of 3

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

Triangles Within Pentagons

Age

14 to 16

Challenge level

3 out of 3

Show that all pentagonal numbers are one third of a triangular number.
problem

Speedy Summations

Age

16 to 18

Challenge level

1 out of 3

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
article
Clever Carl

What would you do if your teacher asked you add all the numbers from 1 to 100? Find out how Carl Gauss responded when he was asked to do just that.