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by philcain

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by philcain

2+2 = 2×2 = 4

1+2+3 = 1x2x3 = 6

What set of four numbers works and what three sets of five numbers?

Four numbers: 1,1,2,4

Five numbers: 1,1,1,3,3; ,1,1,2,2,2; 1,1,1,2,5

by philcain

Can you make a single cut to a cube to make a regular hexagon? If so, how? And what length are the sides of the hexagon if the cube has sides length 1?

Well, perhaps unsurprisingly the answer is, yes you can. Cut through the centre points of the sides like below.

If the cube’s side is length 1, then the hexagon’s sides are the longest side of right angle triangles with side length 1/2. So using Pythagorus, its length is the square root of 2 x (1/4), or √2/2.

by philcain

by philcain

Why does a one-square hole open up when we rearrange these shapes, as shown below?

The longest sides of what appear to be “triangles” are bent. You can read a more thorough explanation here.

I’ll try and come up with a more satisfactory explanation.

by philcain

Can you draw two straight lines to cut the clock dial into two sets of numbers with the same sum? And can you do it with five lines to create six groups with an equal sum?