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$1$ | $6$ | $21$ | $56$ ($B$) |
$1$ | $5$ | $15$ | $35$ |
$1$ | $4$ | $10$ | $20$ |
$1$ | $3$ | $6$ | $10$ |
$1$ | $2$ | $3$ | $4$ |
$A$ | $1$ | $1$ | $1$ |
$M$ | $M+N$ |
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Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?