快猫短视频

#149 All in a spin

Fairground designer Ferris Caroselli has designed a new ride. Six teacups, each with seats for passengers, spin around a giant stationary dinner plate. Each cup sits on a cog that is 1 metre in diameter, which meshes with a 5-metre diameter cog under the plate, so that the cups spin without slipping.

A mother watched her children on the ride, and counted how often they spun around in one full circuit of the plate. She was slightly surprised at the answer. How many times was it?

#148 Much ado about muffins

Solution

2520 muffins. The total number of muffins must be divisible by 9 (the number of bakers) and 8 (the number of flavours). And because the muffins can be split equally between 2, 3, 4, 5, 6 and 7 tables, the total is divisible by those numbers too. Because the number of muffins is the minimum possible to meet these criteria, the total must have the minimum number of factors (in this case, the lowest prime numbers that can generate all the necessary divisors: 2 x 2 x 2 = 8, and 3 x 3 = 9).

These factors are 2 x 2 x 2 x 3 x 3 x 5 x 7 = 2520.