# Who Weighs What Puzzle - Solution

## The Puzzle:

Hungry Horace likes to save money whenever he can (so that he's got plenty left to buy more food) so when he went swimming with some of his friends he had a clever idea to use the weighing machine to weigh him and his two friends for only one 10c coin!

Once the weighing machine has shown a reading the dial can only go down to a lower weight. So this is what Horace did. He and his two friends sorted themselves out in order of weight (they knew that Horace was the heaviest and that Tiny Tim was the lightest), and then followed this plan:

Hungry Horace and Curly Kate put the 10c in and got on the scales.

The dial showed 85 kg

Tiny Tim got on and Curly Kate got off.

The dial went down to 75 kg

Curly Kate got back on and Hungry Horace got off.

The dial went down to 60 kg.

Find the correct individual weights of Hungry Horace, Curly Kate and Tiny Tim.

Once the weighing machine has shown a reading the dial can only go down to a lower weight. So this is what Horace did. He and his two friends sorted themselves out in order of weight (they knew that Horace was the heaviest and that Tiny Tim was the lightest), and then followed this plan:

Hungry Horace and Curly Kate put the 10c in and got on the scales.

The dial showed 85 kg

Tiny Tim got on and Curly Kate got off.

The dial went down to 75 kg

Curly Kate got back on and Hungry Horace got off.

The dial went down to 60 kg.

Find the correct individual weights of Hungry Horace, Curly Kate and Tiny Tim.

## Our Solution:

From the question we know:

(1) Horace + Kate = 85

(2) Horace + Tim = 75

(3) Kate + Tim = 60

(1) and (2) tell us that Curly Kate is 10 kg heavier than Tiny Tim.

So (3) tells us that Tim is 25 kg and Kate is 35 kg.

Similarly we can work out that Hungry Horace is 15 kg heavier than Curly Kate. So Horace is 50 kg.

(1) Horace + Kate = 85

(2) Horace + Tim = 75

(3) Kate + Tim = 60

(1) and (2) tell us that Curly Kate is 10 kg heavier than Tiny Tim.

So (3) tells us that Tim is 25 kg and Kate is 35 kg.

Similarly we can work out that Hungry Horace is 15 kg heavier than Curly Kate. So Horace is 50 kg.

Puzzle Author: Stephen Froggatt