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Difficulty: Tricky

Three new chocolate brands are being released: Jupiter, Astro, and Celeste. A batch of Jupiter bars needs 2 kilograms (kg) of cocoa mass, 2 kg of cocoa butter, and 1 kg of sugar. Astro needs 2 kg of cocoa mass, 2 kg of nuts, and 1 kg each of cocoa butter, sugar, and milk. Celeste needs 1 kg each of cocoa butter, sugar, and milk.

The Chocolate Marketing Board needs to prepare a selection of bars for a taste testing event, but they only have 6 kg of cocoa mass, 7 kg of cocoa butter, 6 kg of sugar, 5 kg of milk, and 4 kg of nuts. How many batches of each chocolate bar do they make to use up all their ingredients?

Scroll down or click for a hint, or the answer!


 

Brainteaser hint

Not all the chocolate bars use all the different ingredients. Try starting with an ingredient only used in one type of bar.

Brainteaser answer

Only Astro needs nuts. There are 4 kg of nuts, and one batch of Astro uses 2 kg of nuts. So 2 batches of Astro need to be made to use up all the nuts.

Astro and Celeste need milk. Two batches of Astro uses 2 x 2 = 4 kg of milk. That means there is 7 – 4 = 3 kg of milk left that needs to be used making Celeste. Each batch of Celeste takes 1 kg, so there are 3 batches of Celeste.

Jupiter and Astro need cocoa mass. Two batches of Astro uses 2 x 2 = 4 kg, which means there is 6 – 4 = 2 kg of cocoa mass left for Jupiter. That’s enough for one batch.

Finally we need to check the other ingredients. If we have one batch of Jupiter, 2 batches of Astro, and 3 batches of Celeste we would need 2 + 2 + 3 = 7 kg of cocoa butter and 1 + 2 + 3 = 6 kg of sugar – exactly what we have.