快猫短视频

#224 Russian dolls

Set by Holly Biming

I collect Russian dolls, the type where each doll can be opened to reveal a smaller one inside. I am particularly fond of my simple, single-coloured ones, which come in sets of five (and, unusually, have a hollow smallest doll). I have five lovely sets of them, each a different colour.

Alas, while I was out, my daughter Kira rearranged them so that each large doll now contains one each of the four other colours. She proudly tells me that no blue doll contains a doll that has a yellow doll anywhere within it. There is no doll that contains a pink doll with a red doll anywhere within it. And no yellow doll contains a green doll with a pink doll anywhere within it.

鈥淏y the way, have you seen my wedding ring?鈥� I ask her.

鈥淎h, I put that inside the smallest blue doll,鈥� replies Kira.

Which coloured doll should I open first if I want to find the ring as quickly as possible?

Solution next week

#223 Setting the right tone

Solution

Leo needs to mix five parts of the first dollop of paint with four parts of the second dollop.

One third of each dollop is always blue, so we only need to consider the yellow and red paint. Each measure of the second dollop has five units of yellow and three of red, for a total of eight. The same measure of the first dollop will give us four units of each.

We want to have yellow and red paint in a ratio of 5:4, which is 40:32 in multiples of 8. Since each measure of the second dollop gives us two more units of yellow paint than red, four measures are required to create a gap of eight units between the two colours (20 yellow, 12 red). Adding five measures of the equal mixture increases this to 40:32. Hence, we need five parts of the first dollop to four of the second.