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Four Math Puzzles

Here are some new math puzzles to test and exercise your brain. I particularly like the first one, because it seems counter-intuitive. The solutions are at the bottom of the page.

Vinegar and Oil

One pitcher has five quarts of oil in it, and another pitcher has five quarts of vinegar. John takes a quart of oil from the first pitcher and mixes it into the pitcher of vinegar. He then takes a quart of this mixture and mixes it back into the pitcher full of oil. Is there now more oil or less oil in the first as there is vinegar in the second?

Adding Up to 100

16,17,23,24,39,40

Adding together each of these numbers as many times as you want, how do you reach a sum of exactly 100?

Adding Up to 1000

Using the digit "8" 8 times (and no other digits), add numbers together to reach a sum of 1000.

Animal Math

A small zoo had just mammals and birds. When asked how many of each they had, the zoo keeper said he had a total of 54 animals with a 140 feet total between them all. Assuming all the animals had all the feet they should have, how many birds and how many mammals were there?

Solutions to the Math Puzzles

Vinegar and Oil

The amounts are the same. After mixing in a quart of oil, the mixture would be 5/6 vinegar and 1/6 oil. A quart removed would be 1/6 oil, then, leaving 5/6 of a quart of oil in the pitcher. Since the other 5/6 of the removed mixture is vinegar, and this is now mixed into the other pitcher, in the end both pitchers end up with 5/6 of a quart of the other liquid in them. If they have equal amounts of the other liquid, and the total volumes are equal (back to 5 quarts each), they must have equal amounts of their original liquids.

Adding Up to 100

16 + 16 + 17 + 17 + 17 + 17 = 100

Adding Up to 1000

8 + 8 + 8 + 88 + 888 = 1000

Animal Math

38 birds (76 legs) and 16 mammals (64 legs).


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