快猫短视频

#71 Dip die

Set by Katie Steckles

A solid, white cube, made from 1-centimetre cubes stuck together, measures 5 cm on each side. How many small cubes are needed to make a cube like this?

The whole cube fell into a bucket of red paint, coating the outside. The cube was then pulled out and separated into its individual cubes to dry. How many small cubes had some paint on them?

Once the paint was dry, the small cubes were placed in a bag. I pulled one out at random, without looking, and rolled it like a dice. What is the probability that, when the cube comes to rest, its top face is red?

Solution next week

#70 Powerful years

Solution

De Morgan was born in 1806. The largest square number less than 1871 is 1849, which is 43 ². (The next-largest square is 1764, but reaching 42 then would have made him 149 at death, which seems unlikely.)

Carrie was born in 2016. She is currently 9 (3²) and will turn 32 (2⁵) in 2048 (2¹¹). If she lives that long, she will be 100 (10²) in 2116 (46²).

People born in 1600 could have turned 81 in 1681.