快猫短视频

#178 Hydra

A story: A hero enters a cave. Inside is a monster with three numbered heads. It attacks! Our hero chops off a head, but two more heads grow in its place. One of the new heads attacks and the hero greets it with a quick chop, too. Standing back, he realises that every chop produces at least one prime-numbered head that, when multiplied by the number on the other new head, gives the number from the head that was chopped. He also notices that all the prime-numbered heads are friendly.

The story鈥檚 illustrator squints at the author鈥檚 scribbled notes. She can make out the number on two of the original three heads, but not the third. Reading ahead, she notices that when the hero collapses triumphant at the feet of the now fully friendly monster, all the heads show different numbers and their sum is 113. 鈥淎ha!鈥� she declares, and draws the original monster with its three snarling, numbered heads. What was the third number?

#177 Monkeying around

Solution

Male and female Equalis monkeys have the same average number of brothers as each other. Although females in all-female families have no brothers, this is balanced out by mixed families that have at least one male, where females have more brothers.

More surprisingly, male and female Fraternis monkeys will also have the same number of brothers as each other, on average. In fact, this is true regardless of the ratio of males to females, even if 99 per cent of offspring are male. Of course, as the proportion of males grows, the average number of brothers also grows (for males and females).