Science Puzzle
The Desert Pack
Two travellers cross a desert. Traveller A has 5 bottles of water and Traveller B has 3. A stranger joins them and all three share the water equally across the whole journey.
At the end, the stranger pays 8 coins for his share. Traveller B says they should split the payment 5 to 3. Traveller A disagrees. Who is right, and what is the correct split?
The Answer
Traveller A is right. The correct split is 7 coins to A and 1 coin to B, not 5 and 3.
Each person drank an equal share of the 8 bottles, which is 8 ÷ 3 = 2⅔ bottles each. Traveller A contributed 5 bottles but consumed 2⅔, so he effectively gave the stranger 5 − 2⅔ = 2⅓ bottles. Traveller B contributed 3 but consumed 2⅔, so he gave the stranger only 3 − 2⅔ = ⅓ of a bottle.
The ratio of their contributions to the stranger is 2⅓ to ⅓, which simplifies to 7 to 1. A 5:3 split counts who brought the most, not who gave the most to the stranger. Reframing the question precisely reveals the answer.
The principle: Reframing perspective. Defining the question precisely changes the answer. The split is not who brought the most, but who gave the most to the person paying.