快猫短视频

#223 Setting the right tone

Set by Mary Ellis

鈥淣ot one of your best, is it?鈥� smirked Michael, peering over Leo鈥檚 shoulder at the portrait he was painting. 鈥淭he colours are so drab. Who is she?鈥�

鈥淭he name鈥檚 Lisa,鈥� said the model, smiling enigmatically from the other side of the easel.

鈥淚鈥檓 trying to mix a glaze to perfect the tone of her face,鈥� sighed Leo. 鈥淏ut I seem to have run out of paint.鈥�

鈥淵es, about that,鈥� said Michael. 鈥淚 might have borrowed some for a ceiling. In any case, it looks like you鈥檝e got two brownish dollops there.鈥�

鈥淥ne of them is equal parts yellow, red and blue. The other is five parts yellow, three parts red and four parts blue. But anyone can see her cheeks require 10 parts yellow, eight parts red and nine parts blue!鈥� said Leo.

Lisa sat and listened quietly, with a knowing look in her eye. Or maybe sad, or bored; it is hard to say. But if Leo is to finish his portrait, in what proportions should the two dollops be mixed to produce the right tone?

Solution next week

#222 A question of balance

Solution

More than 2 kilograms have been weighed.

We can say that the two arms have lengths A and B, and that the first portion of flour is F1 kg, while the second is F2 kg. A 脳 F1 = B, so F1 = B / A. On the other hand, B 脳 F2 = A, so F2 = A / B. So, the total mass is F1 + F2 = B / A + A / B.

Experimenting with some values of A and B should convince you that F1 + F2 is always > 2, but you can use algebra. Subtract 2 kg from the total and rearrange to get: (A² + B² 鈥� 2AB) / AB = (A 鈥� B)² / AB. Since A is a different length to B, (A 鈥� B)² / AB must be > 0, so the total was over 2kg.