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Channel: A Mathematician's Holiday
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Medicine muddle - Encoding and Binary

Given four bottles with indistinguishable liquid, one of which is a vital medicine, two containers and a test that can be done only once, how can you determine which of the the bottles contain the...

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Dim Sum - Coding efficiency

In a restaurant where you can order tasting plates of 10 items, what is the smallest number of plates you can order to identify all 10 items on a menu?

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Fix the Hotel Rooms - Topology

By drawing on a piece of paper, can you connect three houses to three utilities (gas, electricity, water) without any of the lines crossing?

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The Tiny Lift - Graphs

How can you get three people to the upper floor of the hotel if two of them can never be left alone?

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Hotel fire - Optimisation

What is the quickest route to get from where you are standing, collect some water from a river and get to the hotel?

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Bags mix-up- Logic and Decision Trees

Three bags contain 2 t-shirts or 2 hoodies or 1 hoodie and 1 t-shirt, and none are labelled correctly. Can you tell which back belongs to whom by only taking one (random) item from one bag?

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Late for the plane - Abstraction and Optimisation

What is the quickest route between two points, if you can only cross the runways at a perpendicular?

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Airport security - Trilinear Coordinates

How do we measure out 100ml of a liquid using only containers taking quantities of 75ml, 125ml and 200ml?

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Planning the tour - Abstraction and Graph Theory

How do you construct a tour travelling between a number of different cities, but never using the same transport method between two cities more than once?

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