Tim from Ysgol Uwchradd Tywyn
I ruled out anything under £1 because it has got to be
more than 50p. Anything doubled over 50p makes more than
I ruled out anything over £2 because you get change from
the biggest coin, being £2.
Then I ruled out anything ending in anything apart from 0. Because
you can't use coppers.
I was left with: £1.80 £1.60 £1.50
I came to the answer of £1.80 because 60p doubled is
£1.20, add them added together is £1.80.
Meaning the ice cream is £1.20 and the crisps are
Tom from the same school as Tim went about it
in a slightly different way:
The crisps would cost 60p and the ice cream would cost
£1.20 making my solution £1.80
I worked this out by discounting anything below £1.65
based on minimum amount of crisps and double amount of ice-cream
and the no copper coins. 75p, 80p, £1.25,
£1.20, 90p, £1.00, £1.44,
£1.45, l.56, £1.50 and £1.27
I discounted anything that wasn't in the 5x table because of the no
copper coins rule. £3.06 and £1.74
I also discounted anything that wasnt divisible by 3 into a number
in the 5x table because the ice-cream is twice as much as the
crisps and the copper coin rule. £1.85 and
Finally I discounted anything that could be paid with 3 coins or
less. £2.10 and £2.25
Leaving only £1.80
Here is another solution from Hayden
from Davenies School who used the clues in a slightly different
I think the answer is £1.80.
The most valuable coin is £2 so I crossed out answers of
£2 or more.
Then I crossed out any answers that needed copper coins.
Then I worked out that the crisps and ice cream had to cost more
than £1.50 so I crossed more out.
I then crossed out any amount that could be paid with fewer than
This left me with two possible answers: £1.80
As the ice cream costs exactly twice as much as the crisps, the
answer is £1.80.
Morgan and Daniel from Greystoke Primary had
another way again:
Using the clue that you will need more than three coins
we eliminated 75p, £2.25 £1,
£2.10, 80p, £1.50, £1.60,
£1.25, £1.20 and 90p.
After that we moved on to the second clue - 'There must be change
from the most valuable coin'! The most valuable coin is
£2 so we could rule out £3.06
Then we moved onto the clues 'The crisps cost more than 50p' and
'The Ice Cream will cost double what the crisps cost!' Therefore we
could rule out totals under £1.50 ( £1.44,
£1.45 and £1.27)
This left us with four options £1.56,
£1.74, £1.85 and £1.80 We could
rule out £1.50 and £1.74 using the 'You could
pay without using copper coins clue'.
Now we had £1.85 and £1.80 remaining. We
discarded the £1.85 because you can't have a total and a
total half of it!
£1.80 is the solution!
Finally, Daniel and Connall sent in
their solution in the from of a table where they give reasons for
eliminating all the other amounts. You can see their work in
this Word document . This
is very easy to understand, thank you boys.
Thank you, too, to everyone else who sent in a
solution agreeing with the answer of £1.80.
(When this problem was first published on the
site, we made a mistake. We've now
corrected it but would still like to thank all those of you who
wrote to point out our error. Children at Much Wenlock Primary
School, Hotwells Primary School, Downsview School, King Henry VIII
Abergavenny, Brocks Hill Primary School, Eastwood Comprehensive,
Rebecca at Gateway Primary School and Benjamin at Holmead Middle
School all explained that in fact it was impossible to solve.)