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GOT IT Now

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Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

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Reverse to Order

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

Bishop's Paradise

Stage: 3 Short Challenge Level: Challenge Level:1


Drawing the diagonals for each of the shapes and counting shows that an octagon has $20$ diagonals, a hexagon has $9$, a pentagon has $5$ and a quadrilateral has $2$.

This can be used to show that A to D are all correct. A quadrilateral has half as many diagonals as it has sides, not twice as many, so statement E is false.







Alternatively, each vertex in a polygon shares a diagonal with $n-3$ others, if there are $n$ vertices, since it does not share one with itself or either of its neighbours. There are $n$ vertices, so this is $n(n-3)$. But this means we have counted each diagonal twice, so there are $\frac 12 n(n-3)$ in total. This gives the numbers obtained directly above.



This problem is taken from the UKMT Mathematical Challenges.

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