Find the smallest natural number greater than 1 US billion (10^9) that has exactly 1000 positive divisors. (The term divisor includes 1 and the number itself. So, for example, 9 has three positive divisors.) Please note that this is the improper US billion, not the correct UK billion – 10^12

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Maths
Five marbles of various sizes are placed in a conical funnel. Each marble is in contact with the adjacent marble(s). Also, each marble is in contact all around the funnel wall.

The smallest marble has a radius of 8mm. The largest marble has a radius of 18mm. What is the radius of the middle marble?

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Maths
This question was asked today, and the first person I thought of was Chris. I have no answer yet, and the fact that probabilities come into it, means I never will….

A standard pack of cards is thrown into the air in such a way that each card, independently, is equally likely to land face up [...]

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Probabilities
The minute hand of a clock is twice as long as the hour hand. At what time, between 00:00 and when the hands are next aligned (just after 01:05), is the distance between the tips of the hands increasing at its greatest rate?

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Maths
A set of positive integers is defined to be wicked if it contains no three consecutive integers. Count the sets with 0, 1 or 2 elements as wicked sets. Find the number of wicked subsets of the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. If it helps, define good sets as [...]

The towns of Cairo, Ptolemy, and Luxor are equidistant from each other. If a car is three miles from Cairo and four miles from Ptolemy, what is the maximum possible distance of the car from Luxor? Assume the land is flat

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Maths
Ten perfect shooters simultaneously and independently fire at ten ducks. On average, how many ducks are killed?

I am returning to Africa for a few days to tidy up the mess I left behind, so in the meantime, here are a few easy stretching exercises…

1. McToM’s Burgers sell Chicken McChunks in boxes holding 6, 9 or 20 McChunks. Therefore, you could purchase exactly 21 Chunks by purchasing two boxes of size 6 [...]

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Maths
9332621544 3944152681 6992388562 6670049071 5968264381 6214685929

6389521759 9993229915 6089414639 7615651828 6253697920 8272237582

5118521091 6864000000 0000000000 00000000

Express this number in an easier format. If it’s any help, which it isn’t, there are 24 trailing 0’s, and Wolfram Alpha won’t be any help either, but hey – give it a go…

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Maths
When I die, I wish to be buried in a pyramid. A little egotiscal I know, but what the hey! The structure will have a square base and be solidly composed of cubical stone blocks. Each level of the pyramid contains one less block per side as the pyramid rises. I have gathered together an [...]

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Maths