### 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.