You are watching: 8 liter 5 liter 3 liter puzzle
You might remember this puzzle indigenous Die difficult with a Vengeance where Bruce Willis and also Samuel L. Jackson need to diffuse a bomb by put a 4 gallon jug that water on a collection of scales...

Generalised Form
We have actually two solutions above which both provide the same answer of 3 litres. It transforms out the if you do it algebraic the answer walk not have actually the same form and it"s type of coincidence. Lets call the smaller container A and the lager B and work it through.Number 1: empty the 5 litre deserve to into the 3 litre have the right to - leaving 2 litres in the 5 litre can. In other words B - A in BFill the 3 litre can with the 2 litres indigenous the 5 litre deserve to - leave 2 litres in the 3 litre can. Together in an are in A of A - (B - A) = 2A - BFill the continuing to be 1 litre room in the 3 litre have the right to from the 5 litre can. Leaving 4 litres in the 5 litre can. For this reason the amount in B is B - (2A - B) or 2B - 2ASo the generalised kind of equipment 1 is 2B - 2A in B.Number 2: to fill the 3 litre can from the tap. Empty the materials of the 3 litre deserve to into the 5 litre can. Which gives us B - A room in B.Fill the 3 litre have the right to from the tap. Empty the components of the 3 litre have the right to into the 5 litre can. - leaving the 5 litre deserve to full and 1 litre in the 3 litre can. Ie. Removing (B - A) native A pipeline A - (B - A) or 2A - B in A pour away the components of the 5 litre can. To water the 1 litre indigenous the 3 litre have the right to into the 5 litre can. In other words 2A - B in BFill the 3 litre deserve to from the tap. Empty the materials of the 3 litre deserve to into the 5 litre can. Leaving 4 litres in the 5 litre can. In other words A + (2A - B) or 3A - B in B.So the generalised type of equipment 2 is 3A - B in B.There space some restrictions, such together in solution 2; 2APayPalI constantly think it"s arrogant to include a donate button, but it has actually been requested. If I aid you gain a project though, you might buy me a pint! - nigel



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