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# Stair Climb

##### Age 11 to 14 ShortChallenge Level

Scaling the number of stairs run
Boris:     5 steps                  100 - finished
Spike:    4 steps       $\times$20      80 - finished (21 + 80 $\gt$ 99)
Percival: 3 steps                   60 - not finished (38 + 60 $\lt$ 99) Last place

$\times$19      95 (4 steps to go)
76   (21 + 76 = 97 $\Rightarrow$ 2 steps to go) winner

Working out how long each person takes
Boris:    $99$ steps
Spike:    $99 - 21 = 78$ steps
Percival: $99 - 38 =61$ steps

In each time unit, Boris runs $5$ steps, Spike runs $4$ steps, Percival runs $3$ steps.

Boris:    $99$ steps, $99 \div 5 = 19\frac{4}{5}$
Spike:    $78$ steps, $78 \div 4 = 19\frac{1}{2}$
Percival: $61$ steps, $61 \div 3 = 20\frac{1}{3}$

Therefore they finish in the order Spike, Boris, Percival.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.