Hex

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

Plex

Plex lets you specify a mapping between points and their images. Then you can draw and see the transformed image.

Transformation Game

Why not challenge a friend to play this transformation game?

Weekly Problem 7 - 2006

Stage: 3 Challenge Level:
$9$ hours.

$$\frac{\text{time taken to dig a bed of diameter six metres}}{\text{time taken to dig a bed of diameter four metres}}=\frac{6^2}{4^2}=\frac{3^2}{2^2} = \frac{9}{4}$$
Hence the time taken for one gardener to dig a bed of diameter six metres is $\frac{9}{4} \times4 \; \text{hours} = 9 \; \text{hours}$

The time taken for six gardeners to dig six flower beds is the same as the time it takes one gardener to dig one bed of the same size, and hence the answer is $9$ hours.

This problem is taken from the UKMT Mathematical Challenges.

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