Worked solutions to:

I/2011/13

I/2015/12

I/2008/12

I/2014/13

I/2016/13

II/2016/13

Worked solutions to:

I/2011/13

I/2015/12

I/2008/12

I/2014/13

I/2016/13

II/2016/13

Question: I choose at random an integer in the range 10000 to 99999, all choices being equally likely. Given that my choice does not contain the digits 0, 6, 7, 8 or 9, show that the expected number of different digits in my choice is 3.3616. Continue reading

A prison consists of a square courtyard of side b bounded by a perimeter wall and a square building of side a placed centrally within the courtyard. The sides of the building are parallel to the perimeter walls.

Guards can stand either at the middle of a perimeter wall or in a corner of the courtyard.

If the guards wish to see as great a length of the perimeter wall as possible, determine which of these positions is preferable.

You should consider separately the cases b < 3a and b > 3a.

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