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Alternatively the task could be used as an exercise in group work - give one member of the group a pen and paper, and give each of the others one (or two) clues. They must not show the clues to anyone or write them down. They can read clues out or explain them to the group. Each student is responsible that their clues are satisfied. The group needs to work together to find a solution to all the clues.
Are you considering ALL possibilities, or just trying to spot something that works?
Coins
Age 11 to 14
Challenge Level 
Why do this problem?
This problem requires students to work systematically and apply some understanding of primes. It could also be adapted as a basis for work familiarising students with UK coinage.Possible approaches
This task could be a suitable homework or "Problem of the Week" during a topic on Probability, Money or Primes. Solutions to the extension questions could be posted on a display board where students could check them and contribute further ideas over an extended period of time.Alternatively the task could be used as an exercise in group work - give one member of the group a pen and paper, and give each of the others one (or two) clues. They must not show the clues to anyone or write them down. They can read clues out or explain them to the group. Each student is responsible that their clues are satisfied. The group needs to work together to find a solution to all the clues.
Key questions
Can you choose a good clue to start working on, one that gives you enough information to get started?Are you considering ALL possibilities, or just trying to spot something that works?
Possible extension
This could be a good time to talk about the phrase "necessary
and sufficient". Ask students to devise a set of clues that define
a unique set of coins, and where no individual clue can be deleted
without losing the uniqueness of the solution.
Possible support
Students could be given a pile of coins, (or a worksheet
ofphotocopied/drawn coins) and asked to select sets of 5 coins from
these, satisfying suitable clues - the total is...
an even number
one more than a multiple of 7
less than 10
all the coins are different, etc.
They could be asked to devise clues for each other, or to look
for combinations of clues that define one specific set of
coins.
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