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Guarding the castle brainteaser

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Difficulty: Tricky

Square with three circles containing the number 4 on each side.

12 soldiers guard each wall

There are 32 soldiers guarding a square castle. The castle has 8 towers – one in each corner of the square, and one in the middle of each side. The soldiers want to make sure all the walls are guarded.

Initially, 4 soldiers went to each tower to stand guard. That way, along each side of the square there were 12 soldiers: 4 in the first corner, 4 in the middle tower and 4 in the other corner.

Square with three circles along each side.

Can you guard the castle?

After a few days, the soldiers realised they had chores that needed doing. Their uniforms were starting to smell, their water flasks were almost empty, and someone really needed to empty the toilet buckets. One soldier from each tower got stuck with all the chores.

Meanwhile, the remaining 24 soldiers kept guarding. But now each side only had 9 guards along it. The soldiers were starting to get scared, until one soldier had a clever idea. They moved some soldiers around, then suddenly there were 12 soldiers along each edge of the square castle.

Can you work out how to arrange the 24 soldiers?

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

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Brainteaser hint

It’s a big task covering 8 missing soldiers. The key to this puzzle is that not all the towers are equal. Choose your towers carefully!

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Brainteaser answer

Square with three circles along each side, the corner circles have the number 6 and the sides 0.

Here’s one solution


A soldier in the middle of a side of the castle is only protecting that side. One stationed in a corner tower is protecting two sides!

Clearly, it’s a good idea to put soldiers into the corner towers. One solution is to put 6 soldiers in each corner tower. There are 4 corners, so it takes 6 x 4 = 24 soldiers, and along each side there are 6 + 0 + 6 = 12 soldiers.

This isn’t the only solution – how many can you find?
 

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