1 

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 medicine? 
Thomas Woolley, William Binzi 
24 Oct 2014 
2 

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? 
Thomas Woolley, William Binzi 
24 Oct 2014 
3 

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? 
Thomas Woolley, William Binzi 
24 Oct 2014 
4 

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? 
Thomas Woolley, William Binzi 
24 Oct 2014 
5 

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? 
Thomas Woolley, William Binzi 
24 Oct 2014 
6 

Bags mixup Logic and Decision Trees 
Three bags contain 2 tshirts or 2 hoodies or 1 hoodie and 1 tshirt, and none are labelled correctly. Can you tell which back belongs to whom by only taking one (random) item from one bag? 
Thomas Woolley, William Binzi 
24 Oct 2014 
7 

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? 
Thomas Woolley, William Binzi 
24 Oct 2014 
8 

Airport security  Trilinear Coordinates 
How do we measure out 100ml of a liquid using only containers taking quantities of 75ml, 125ml and 200ml? 
Thomas Woolley, William Binzi 
24 Oct 2014 
9 

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? 
Thomas Woolley, William Binzi 
24 Oct 2014 