There are people stood in a line, each with either a black or a white hat on. Why not learn about modular arithmetic, and try to figure out why? Repeat this process down the line to save Person 4,Person 6, Since , I have been employed by the School of Mathematics and Statistics in a teaching-focussed role. One by one, moving down the line, they have to say one word – either black or white. While the initial wave of strike action is over, the dispute has not been resolved, and there is likely to be more disruption after Easter, comparable to the first wave of strikes, unless a solution is found.

Solution Saving half of them is easy! There are integers and pigeon-holes, so by the pigeon-hole principle there are two numbers in the same pigeon-hole. However, we can do significantly better by following the strategy below. Person 2 looks at the remaining 98 hats and counts the number of white hats. Since , I have been employed by the School of Mathematics and Statistics in a teaching-focussed role.

## Sam Marsh, University Teacher

This is, of course, totally obvious, but it is surprisingly useful. However, we can do significantly better by following nick gurski thesis strategy below. More Perhaps even more surprisingly, this problem can be extended further: While the initial wave of strike action is over, the dispute has not been resolved, and there is likely to be more disruption after Easter, comparable to the first wave of strikes, unless a solution is found.

The implementation was highly successfuland resulted in a Senate Award for Collaborative Activities from the University of Sheffield and a runner-up place in the Teaching Excellence category of the Guardian University Awards. In other words, how many people can you save? So we have saved 99 of the people. If Nick gurski thesis interviewed you at an open-day nick gurski thesis left you a brainteaser or problem to think about, then look below for a reminder of the problem and the solution.

Person nick gurski thesis says the colour of Person 2’s hat and may die ; then Person 2 knows their own hat colour, so can save themself. Person 2 looks at the remaining 98 hats and counts the number of white hats.

The question is, what’s the best strategy to pick? As a reminder, the pigeon-hole principle is the following statement.

nick gurski thesis Solution Saving half of them is easy! There are integers and pigeon-holes, so by the pigeon-hole principle there are two numbers in the same pigeon-hole.

I was part of a team which introduced a flipped approach to our Level 1 engineering teaching in Septemberbased around videos and active small-group sessions.

I am the communications officer for Sheffield UCU, previously holding the role nick gurski thesis pensions officer.

Label pigeon-holes with the numbers 0, 1. Now, the people were allowed to devise a strategy before being given the hats. Perhaps even more surprisingly, this problem can be extended further: There are people stood in a line, each with either a nick gurski thesis or nick gurski thesis white hat on.

Can you prove it?

Show solution Solution Saving half of them is easy! Let Person 1 count the number of white hats they can nick gurski thesis. Using the information from Person 1, they can deduce with certainty the colour of their own hat, so are saved. But spare a thought for Person 1. Due to planned major downgrades to pensions of academic staff, members of the University and College Union have been striking at universities around the country.

If the colour they say matches that of their hat, they survive, otherwise they die. If we take one number from the other we will end up with something that has zero remainder on division by One by one, moving down the line, nick gurski thesis have to say one word – either black or white.

You can read more about the reasons for the dispute hereand you can also read an article I was asked to write for the Times Higher Education Supplement here. Each person can see everybody else’s hat, but nick gurski thesis their own. Here’s a statement which looks like some difficult number theory, but just comes down to the pigeon-hole principle.

I can be found in room G9 of the Hicks Building. Otherwise, they say ‘black’. Repeat this process down the line to save Person 4,Person 6, I nick gurski thesis also interested in developing a broad skills base for our students, and was nick gurski thesis in the creation and subsequent delivery of our Mathematical Investigation Skills module, which introduces first-year students to programming, web-design and mathematical writing, and has proven to be popular and well-received.

SinceI have been employed by the School of Mathematics and Statistics in a teaching-focussed role.

### Sam Marsh, University Teacher

Why not learn about modular arithmetic, and try to figure out why? But in fact, the same works for Person 3, Person 4, I’ve been at the University of Sheffield sincefirst as an undergraudate then as a PhD student of Neil Strickland. If Nick gurski thesis 1 sees an odd number, then they say ‘white’.