Question

Tom has six banknotes.

The value of each note is £5 or £10 or £20
He can make £20 with three notes.
He can make £55 with four notes.
He cannot make £25 with three notes.
He cannot make £25 with four notes.
List the six notes from smallest value to largest value.
£
£
£
£
£
£ _
Smallest
Largest
Total marks: 2

Answer 1

£5, £5, £10, £20, £20, £20.

Explanation:

To make £20 with 3 notes he uses 2 5's and a 10 . That is the only way he can make £20 with 3 notes.

To make £55 with 4 notes he could use 2 £20's , £10 and a £5. That is the only way to make £55 with 4 notes.

So the possible list is:

20, 20 ,10 ,5, x, y where x and y are the 2 extra notes.

He cannot make £25 with 3 notes so neither x nor y is £10.

He cannot make £25 with 4 notes so x and y cannot both be £5. But 1 must be £5 because he needs 2 £5 to make the £20.

So one must be £5 and the other must be £20.