A shepherd has sheep, goats, and cows. All of them except 12 are sheep, all of them except 14 are goats, and all of them except 16 are cows. How many animals does the shepherd have in total?
21
Let S be sheep, G be goats, C be cows, and T be total. T - S = 12, T - G = 14, T - C = 16. The sum of these differences is (T-S) + (T-G) + (T-C) = 3T - (S+G+C) = 12 + 14 + 16 = 42. Since S+G+C = T, 3T - T = 42, so 2T = 42, meaning T = 21.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Medium. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
More logic riddles
Two sisters were born at the exact same hour on the exact same day of the exact same year to the same biological parents, yet they are not twins. How can this be?
If five machines can make five widgets in exactly five minutes, how many minutes would it take one hundred machines to make one hundred widgets?
Two people share me on a plate with two forks and candlelight. What am I?
A locked wooden box contains three coins. Exactly one is genuine (correct weight), one is heavier than genuine, and one is lighter than genuine. You have a pan balance and are allowed exactly two weighings. Can you definitively identify the genuine coin?
You write me, sign me, and send me to someone you care about in February. What am I?
A security guard sleeps during the day and works at night. One Tuesday afternoon, he hears a loud crash outside his window. He wakes up immediately, looks out, and arrests a neighbor for vandalism. Why was he arrested?