Ten Problems

13, 18, 21, 22, 23
13, 19, 20, 22, 23
14, 15, 21, 23, 24
14, 16, 20, 23, 24
14, 16, 21, 22, 24
14, 17, 19, 23, 24
14, 17, 20, 22, 24
14, 18, 19, 22, 24
14, 18, 20, 21, 24
15, 16, 17, 24, 25
15, 16, 18, 23, 25
15, 16, 19, 22, 25
15, 16, 20, 21, 25
15, 17, 18, 22, 25
15, 17, 19, 21, 25
15, 18, 19, 20, 25
16, 17, 18, 20, 26
B) There are twice as many insect legs as there are bird legs (clue 4). To find the possible bird and insect group sizes, multiply the quantity of insects by 6 (legs per insect). Subtract 2 (an insect is missing 2 legs). Divide by 2 (twice as many insect legs as bird legs). Divide by 2 (legs per bird) to get the quantity of birds. The formula is: B = ((I * 6) - 2) / 4. There are three combinations that work: 13 and 19, 15 and 22, 17 and 25.
((13 insects * 6 legs/insect) - 2 missing legs) / 4 = 19 birds
((15 insects * 6 legs/insect) - 2 missing legs) / 4 = 22 birds
((17 insects * 6 legs/insect) - 2 missing legs) / 4 = 25 birds
Of the 17 sets (from step A), only 5 contain these sizes.
13, 19, 20, 22, 23 (13 insects & 19 birds)
15, 16, 17, 24, 25 (17 insects & 25 birds)
15, 16, 19, 22, 25 (15 insects & 22 birds)
15, 17, 18, 22, 25 (15 insects & 22 birds or 17 insects & 25 birds)
15, 17, 19, 21, 25 (17 insects & 25 birds)
C) There are as many snake heads as spider heads (clue 5). Since there is a snake with two extra heads, there are actually 2 fewer snakes compared to spiders. Only 2 combinations (from step B) yield the required head count.
13 insects, 19 birds, 20 snakes, 22 spiders, 23 mammals
15 mammals, 17 insects, 19 snakes, 21 spiders, 25 birds
D) The only group combination (from step C) that produces 376 legs (clue 1) is: 15, 17, 19, 21, 25. The other combination yields 380 legs.
(15 mammals * 4 legs/mammal) - 1 missing leg = 59 legs
(17 insects * 6 legs/insect) - 2 missing legs = 100 legs
19 snakes * 0 legs/snake = 0 legs
(21 spiders * 8 legs/spider) - 1 missing leg = 167 legs
25 birds * 2 legs/birds = 50 legs

Thus, there are: 19 snakes (21 heads and 0 legs), 25 birds (26 heads and 50 legs), 15 mammals (15 heads and 59 legs), 17 insects (17 heads and 100 legs), and 21 spiders (21 heads and 167 legs). This produces 97 animals with 100 heads and 376 legs.

An animal cracker

The woman was playing the game “Monopoly”

Three birds were seen by one person each, three were seen by each unique pair (Abel-Mabel, Abel-Caleb, and Mabel-Caleb), and one was seen by all three. So seven birds were seen in all, and each person saw a total of four. Hence, all of the birds Caleb saw were yellow. These four birds are: (1) the one Caleb saw alone, (2) the one Caleb saw with Abel, (3) the one Caleb saw with Mabel, and (4) the one all three saw together. This accounts for both of the yellow birds Abel saw, and two of the three yellow birds Mabel saw. The third yellow bird Mabel saw could not have been the one Abel and Mabel saw together, because Abel only saw two yellow birds; so the third yellow bird Mabel saw must have been the one she saw alone. So five yellow birds were seen (the one Mabel saw, the one Caleb saw, the one Abel and Caleb saw, the one Mabel and Caleb saw, and the one all three saw), and two non-yellow birds were seen (the one Abel saw and the one Abel and Mabel saw) by the group.

In each pair below, the group 1 saying is listed first.Look before you leap. He who hesitates is lost.
Two heads are better than one. If you want something done right, do it yourself.
The road to hell is paved with good intentions. It’s the thought that counts.
Clothes make the man. Don’t judge a book by its cover.