I went for a drive, and curiosly discovered that my car (Kevin the Capri) only has three speeds. It travels downhill at 72 mph (miles per hour), on the level at 63 mph, and uphill at only 56 mph Kevin the Capri takes 4 hours to travel from Tomsville in Tomshire to Tomerton in Tomerset. [...]Tags: Maths
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 – 10^12Tags: 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?
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?Tags: Maths
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 flatTags: Maths
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 [...]
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…
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 [...]Tags: Maths
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. [...]Tags: 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 [...]Tags: Maths, Probabilities