Creating and manipulating expressions and formulae

problem

Seven Up

Age

11 to 14

Challenge level

3 out of 3

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?
problem

Quick Times

Age

11 to 14

Challenge level

3 out of 3

Can you verify and generalise these equations?
problem

Adding in Rows

Age

11 to 14

Challenge level

3 out of 3

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
problem

Please Explain

Age

11 to 14

Challenge level

3 out of 3

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain why this works.
problem

Top-Heavy Pyramids

Age

11 to 14

Challenge level

3 out of 3

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

Algebra Match

Age

11 to 16

Challenge level

1 out of 3

A task which depends on members of the group noticing the needs of others and responding.
problem

What Does It All Add Up To?

Age

11 to 18

Challenge level

2 out of 3

If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
problem

eNRICHing Experience

Age

14 to 16

Challenge level

1 out of 3

Find the five distinct digits N, R, I, C and H in the following nomogram
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

Powers of Four

Age

14 to 16

Challenge level

1 out of 3

Can you work out the value of x in this 'power-full' equation?