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Which is a better fit, a square peg in a round hole or a round peg in a square hole?

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If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

Mixing Paints

Age 11 to 14 Challenge Level:

Experiment with different combinations of paints A and B (and paints C and D).


The ratio $1:4 = 2:8 = 3:12 = 4:16$ ...

The ratio $1:5 = 2:10 = 3:15 = 4:20$ ...


B is whiter than A (and D is whiter than C), so what will be special about the combinations that achieve the paler shades of pink?