Mind games 15: Answers

38. What am I?

123 = CAB

2345 = ABBA

456 = BAG

567 = AGE

Put them all together - I’m a CABBAGE!

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39. Befuddled besiegers

Lay a plank across one corner of the moat. Then lay a second plank from the middle of the first plank onto the island. Careful now: your army will have to tread cautiously when they storm this castle. Those planks are very carefully balanced.

Not convinced it can be done? If you want mathematical proof, this puzzle can be worked out with simple calculations using the Theorem of Pythagoras – which, you may recall, goes like this:

In a right-angled triangle, the area of the square on the hypotenuse (c) is equal to the sum of the areas of the squares on the other two sides (a and b).

The “hypotenuse” is the side of the triangle opposite the right angle.

This ancient theorem is named after Pythagoras of Samos (c.570–c.495 BC), the Greek philosopher who was the first to prove it.

When you lay the first plank down, it forms a right-angled triangle with the sides of the moat. The diagonal distance from the corner of the moat to the corner of the island can also be seen as the hypotenuse of another right-angled triangle.

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References:
Guthrie, W. K. (1979) A History of Greek Philosophy: Earlier Presocratics and the Pythagoreans Illustration of the Pythagorean Theorem: Wikimedia Commons

And thanks to Kyle Boshoff for the cabbage!