An a × b × c cuboid is constructed out of abc identical unit cubes, sort of like Rubik’s Cube, but not necessarily square (I felt I needed to say that). Divide the cuboids into two mutually exclusive types: External cubes are those that constitute the faces of the cuboid; Internal cubes are completely enclosed. [...]

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Maths
Twenty-seven identical white cubes are assembled into a single cube, the outside of which is painted black. The cube is then disassembled and the smaller cubes thoroughly shuffled in a bag. A blindfolded man (who cannot feel the paint) reassembles the pieces into a cube. What is the probability that the outside of this cube [...]

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Maths,

Probabilities
Will the first day of a century fall on a Sunday, when was the last time? That’s it, simple as that.

But do a bit of research, yes, the calendar follows a predictable pattern, and so do the days of the week. Since first days of the century occur so rarely (oh, about every 100 years [...]

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Tom
An urn contains a number of coloured balls, with equal numbers of each color. Adding 20 balls of a new color to the urn would not change the probability of drawing (without replacement) two balls of the same color.

How many balls are in the urn? (Before the extra balls are added.)

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Probabilities
Using only the numbers 1, 3, 4, and 6, together with the operations +, −, ×, and ÷, and unlimited use of brackets, make the number 24. Each number must be used precisely once. Each operation may be used zero or more times. Decimal points are not allowed, nor is concatenating digits, as in 3 [...]

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Maths
Two players play the following game with a fair (!) coin.

Player 1 chooses and announces a sequence of 3 heads and tails (HHH, HHT, HTH, HTT, THH, THT, TTH, or TTT) that might result from three successive tosses of the coin.

Player 2 then chooses a different sequence of three.

The players toss the coin until one [...]

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Coin flips