Fill a tank to exactly 17 litres with two jugs

Question

An aquarist needs to add exactly 17 litres of treated water to a large empty tank. All she has is a 7-litre jug and a 3-litre jug, both unmarked, and a tap. She can fill either jug to the brim and tip it into the tank, but she cannot read the water line on the jugs or on the tank. Neither jug is anywhere near 17 litres, and the tank has no markings of its own. How does she pour in precisely 17 litres?

Accepted Answer

Because the tank only ever receives whole jugfuls, the amount inside is some total of 7s and 3s. So the question becomes: can 17 be written as 7m + 3n with m and n whole numbers? Yes, 17 = 7 + 7 + 3, that is m = 2 and n = 1. So the recipe is simply: 1. Fill the 7-jug and empty it into the tank. Tank now holds 7. 2. Fill the 7-jug again and empty it into the tank. Tank now holds 14. 3. Fill the 3-jug and empty it into the tank. Tank now holds 17. Three pours, done. Note that neither jug alone lands on 17, five 3-jugs give 15 and a sixth overshoots to 18, while two 7-jugs give 14 and a third ov…

Fill a tank to exactly 17 litres with two jugs

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