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## 'Countdown Fractions' printed from http://nrich.maths.org/

This is a more challenging version of

Countdown
Choose any 6 cards.

The top row always contains the numbers 1, 2, 3 and 4 and the
bottom row contains a range of fractions, that changes according to
the level of difficulty:

- Level 1: halves, quarters and eighths
- Level 2: halves, thirds, quarters, sixths and twelfths
- Level 3: halves, quarters, fifths, tenths and twentieths
- Level 4: halves, thirds, quarters, fifths, sixths, tenths,
twelfths, fifteenths, twentieths, thirtieths and sixtieths.

Select a level and click on "play" to set a target. The
challenge is to hit the target with the numbers available using
just addition and subtraction.

Each card can only be used once. It may not be necessary to use all
the cards.

It is always possible to hit the target. Clicking on "Show a
solution" will offer one possible way in which the target can be
reached, but it will not necessarily be the most efficient
solution.

You may like to take on the challenge on your own or choose to play
it as a game in which the first to reach the target gets a point.
First to 10 points wins.

An alternative game could set a time limit and require the players
to get as close to the target as possible. Each player could start
with 20 points and then points could be deducted according to how
far from the target each player has reached - e.g.$\frac{1}{4}$
away from the target would mean that $\frac{1}{4}$ of a point was
deducted. After a set number of rounds, the player with the highest
score wins.

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