Working systematically
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problemEggs in baskets
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?
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problemTwo on five
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
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problemThe Pied Piper of Hamelin
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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problemElf suits
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last? -
problem1 to 8
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line. -
problemEight queens
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others. -
problem5 on the clock
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
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problemBell ringing
Suppose you are a bellringer. Can you find the changes so that, starting and ending with a round, all the 24 possible permutations are rung once each and only once? -
problemTake a message soldier
A messenger runs from the rear to the head of a marching column and back. When he gets back, the rear is where the head was when he set off. What is the ratio of his speed to that of the column?