Did you solve it? Logicians in a line
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The answer to today’s queueing condundrum. Earlier today I set you the following logic problem, as a retrospective commemoration of World Logic Day. Here it is again with the solution – and a comment about how it relates to the real world. Queue eye. 1. Ten logicians are put in a line, all facing in the same direction. A red or green hat is put on each of their heads. The logicians do not know which colour is on their heads, nor the colour of the hats of the people behind them in the line. Each logician can look only forwards, and so only knows the hat colour of the person or people in front them.
One by one, each logician says aloud either the word ‘red’ or the word ‘green’. Every logician says one of these words, and no logician speaks twice. Can you think of a strategy – which the logicians will have agreed on before the line up – that results in at least nine of them saying the colour word that correctly describes the hat on their head?.
There are no mirrors or reflective materials. The knowledge about their own hat colour is deduced entirely from what they can see and what is said. 2. The same set up as before, but now there are three hat colours: red, green and yellow. Can you think of a strategy in which each logician says a single word, now either ‘red’, ‘green’ or ‘yellow’, and results in at least nine of them saying the correct colours of their own hats.
Solution. 1. Here is a strategy that works. The first person to speak is the person at the back of the line. Second is the person directly in front of them, and so on until the person in the front of the line is the last person to speak. The person at the back of the line may or may not say the correct colour of their hat, but everyone else will.
