Required Mathematical Intelligence

Chapter 144 The Number of Dragonflies

There are 18 spiders, dragonflies, and cicadas in total, with 118 legs and 20 pairs of wings (spiders have 8 legs; dragonflies have 6 legs and two pairs of wings; cicadas have 6 legs and a pair of wings), how many dragonflies are there? Only?
[Answer: This is a question of development and change on the basis of chickens and rabbits in the same cage.Observing the characteristics of numbers, both dragonflies and cicadas have 6 legs, and only spiders have 8 legs.Therefore, we can start with the number of legs to find out the number of spiders.We assume that all three animals have 6 legs, then the total number of legs is 6×18=108 (pieces), and the difference is 118-108=10 (pieces), which must be caused by undercounting the number of legs of the spider.Therefore, there should be (118-108) ÷ (8-6) = 5 (only) spiders.

这样剩下的18-5=13（只）便是蜻蜓和蝉的只数。再从翅膀数入手，假设13只都是蝉，则总翅膀数1×13=13（对），比实际数少20-13=7（对），这是由于蜻蜓有两对翅膀，而我们只按一对翅膀计算所差，这样蜻蜓只数可求7÷（2-1）=7（只）。

Solution: ①Assuming that spiders also have 6 legs, how many legs do the three animals have? 6×18=108 (bars)

②有蜘蛛多少只？（118-108）÷（8-6）=5（只）

③How many dragonflies and cicadas are there? 18-5=13 (only)

④Assuming that the dragonfly is also a pair of wings, how many pairs of wings are there? 1×13=13 (pairs)

⑤蜻蜒多少只？（20-13）÷（2-1）=7（只）

Answer: There are 7 dragonflies. ]
(End of this chapter)