Melon Weight Riddle: 2 kg Plus a Third of Its Own Weight

The melon weighs 3 kg. Its whole weight is 2 kg plus one third of itself, so those 2 kg must be the other two thirds, which makes one third 1 kg and the whole melon 3 kg.

The riddle: a melon weighs 2 kg plus one third of its own weight. How much does the whole melon weigh?

Why is the answer 3 kg?

Picture the melon cut into three equal slices. The riddle says the full weight is 2 kg plus one of those slices. That means the remaining two slices together weigh 2 kg. Each slice is therefore 1 kg, and three slices make 3 kg.

You can check it in one line: one third of 3 kg is 1 kg, and 2 kg plus 1 kg is 3 kg. The riddle's sentence comes out true, and no other weight does that.

What are the usual wrong answers?

The second row is the most tempting trap: a third of its own weight means a third of the unknown.

How can you solve self-referring weight riddles?

Call the weight W and turn the words into an equation: W = 2 + W ÷ 3. Take W ÷ 3 from both sides and you get two thirds of W = 2, so W = 3. The slice method above gives the same result.

A classic balance puzzle, finding the one lighter coin among identical-looking coins in the fewest weighings, first appeared in 1945 ^[1]. Number facts can hide puzzles too: the squares of 1 to 24 add up to exactly 70 squared, and a 1918 result showed that, apart from 1 by itself, 1 to 24 is the only run of squares starting at 1 that adds up to a square ^[2].

Ready for another number riddle?

Each riddle below hides a simple rule behind tempting wording.