Prison Breakout ***

It is lights-out time at the prison where 50 prisoners are locked in 50 cells.  Not realizing the cells' doors are locked, a guard comes along and turns to key to each cell once, unlocking them all.  Ten minutes later a second guard comes along and turns the keys of cells 2, 4, 6, and so on.  A third guard does the same, stopping at cells 3, 6, 9...  This carries on until 50 guards have passed the cells.  How many prisoners can escape?

Look out for a pattern that will give you a shortcut to solving this problem.

Around the Clock Solution

6 - Since Tom runs one and a half times as fast as Jerry, Tom moves round the clock 3 places for every two for Jerry.  We can consider their progress in the table below:

	Position on clock face
Tom	12	3	6	9	12	3	6
Jerry	6	8	10	12	2	4	6

Around the Clock *****

Tom is at 12 o’clock and Jerry is at 6 o’clock.  (Think of a clock.)  At the same time, they both start to run clockwise, with Tom running one and a half times as fast as Jerry.  At which number do they first meet?

Sergeant's Orders Solution

South – After every four right turns the troops will be facing north again; so after 68 turns they are facing north, after 69 turns east, and after 70 turns south.

Sergeant's Orders ***

A sergeant stands too long in the sun and gets confused.  His troops are lined up facing north.  The he gives the order to “Turn right” 70 times, and his troops do so.  In which direction are the troops facing at the end?

More questions to ponder... Solutions

1. 1 km = 1000m = 1, 000, 000 mm

2. 180m (With 10 posts there are only 9 gaps between posts.)

3. 79  - Between 1 and 100 there are 98 numbers and 19 of those numbers have a 9 in them so there are 79 numbers which do not have a nine.