This page is dedicated to problem solving with problems found from the internet

The first two were found on the mathmistakes website.

1. You need exactly four gallons of water, yet you only have two buckets: one five gallons and the other seven. How do you measure out four? Can you measure every number of gallons from one to twelve? How?

Answer:

Fill the 7 gal with water, use it to
fill the 5 gal leaving 2 in the 7 gal. Dump the 2 into the 5,
the refill the 7. Fill the 5 gal the rest of the way with the
7 gal, leaving four left over. Now try getting 7 gallons using
a 4 gallon and a 9 gallon bucket.

2. A box that is 6 inches in length, 5 inches in width and 6 inches high. There is a spider in the top right front corner. There is a fly in the opposite bottom left rear corner. What is the shortest path necessary for the spider to walk, and how far will it walk?

Answer:

If you flatten the box into a flat plane you end up with a 12 by 5 rectangle, and if the spider walks a beeline diagonally across this rectangle, then using the Pythagorean Theorem, he only walks 13 inches. Nice and even right? Well, dozens of people have written in saying the answer is wrong. The flattened box could also create an 11 by 6 triangle which has a hypotenuse of 12.53 inches. Note the following illustration: