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14 Divisors

What is the smallest number with exactly 14 divisors?

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Summing Consecutive Numbers

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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Helen's Conjecture

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

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Stage: 3 Challenge Level: Challenge Level:1

In the following grid, how many pairs of numbers can you find that add up to a multiple of 11?
 

9 46 79 13
64 90 2 97
25 31 20 22
4 52 55 7

Do you notice anything interesting?

Can you find all the pairs?

Could you convince someone that you haven't missed any?

Here is another grid. This time we are interested in pairs that add up to a multiple of 13. How can you use your insights from above to find all the possible pairings?
 

11 54 93 15
76 106 2 115
29 37 24 26
4 62 65 9


Thank you to Susanne Mallett from Comberton Village College for introducing us to this problem.


Click here for a poster of this problem.