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Sums of Squares

Prove that 3 times the sum of 3 squares is the sum of 4 squares. Rather easier, can you prove that twice the sum of two squares always gives the sum of two squares?

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Double Time

Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.

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Given the mean and standard deviation of a set of marks, what is the greatest number of candidates who could have scored 100%?

Whose Line Graph Is it Anyway?

Age 16 to 18 Challenge Level:
How might you rule out certain pairs of graphs and equations?

Where are the key points on each graph?

For each process, roughly what shape graph would you expect?

Which graphs or equations might be consistent with this?

Once you have matched a process, equation and graph how would you construct very convincing evidence that the match is correct?