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## Chocolate choice brainteaser

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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.

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.

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