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Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

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The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?

Good Work If You Can Get It

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A job needs three men to work for two weeks ($10$ working days).

Andy works for all $10$ days.
Bert works for the first week and Clive works for the second week.
Dave works for $6$ days, but then is too sick to work.
Eddy takes his place for $3$ days, then Fred does the last day.

money

When the job is finished they are all paid the same amount. At first they could not work out how much each man should have, but then Fred says:

"If I give my wages to Andy, and Eddy gives £$100$ to both Dave and me, then the wages will be correct".

How much was paid for the whole job, and how much does each man get?