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Santa scramble

By Elizabeth Thomsen, 5 December 2022

Difficulty: Tricky

To cover the whole world in one night Santa is setting up warehouses of presents around the world. From a base in Singapore on the equator, he sent out 2 sleigh teams. One goes east, and the other goes west, until they meet.

One team has old, slow reindeers, and the other has young, fast reindeers. The fast team goes 50% faster than the slow team.

If the equator is 40,000 kilometres long, how far away from Singapore are they when they meet?

Scroll down or click for a hint, or the answer!


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Brainteaser hint

When the slow team has gone 100 kilometres, how far has the fast team gone? And what’s the total distance that the two teams have covered?

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Brainteaser answer

The 2 teams will meet when the total distance they’ve covered is 40,000 kilometres.

When the slow team goes 100 kilometres, the fast team goes 100 + 50% of 100 = 150 kilometres. In total the 2 teams have gone 250 kilometres.

If we multiply that by 4, the slow team covers 100 x 4 = 400 kilometres and the fast team covers 150 x 4 = 600 kilometres for a total of 1,000 kilometres.

If we multiply by another 40, the total will become 40,000 kilometres, exactly what we want. The slow team covers 400 x 40 = 16,000 kilometres, while the fast team covers 600 x 40 = 24,000 kilometres.

When they meet, they’re 16,000 kilometres from Singapore (as long as you go the short way around the world).

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  1. The way I worked it out was:

    Set the distance the slow team travels to X
    The fast team’s speed is 50% faster, meaning they’ll tavel 50% further, so that’s 1.5X
    The total distance tavelled by both of them = 2.5X, and that’s equal to 40,000

    2.5X = 40,000 — divide both sides by 2.5
    X = 16,000


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