November / December
Q: Four men must cross a rickety footbridge at night. Many planks are missing and the bridge can only hold 2 men at a time, otherwise it will break. The men must use a flashlight to guide themselves across because of missing planks. There is only one flashlight. The men travel at different speeds. John can cross one way in 1 minute, Bill in 2 minutes, Ralph in 5 minutes, but Chuck needs 10 minutes to cross the span. As luck would have it, in 17 minutes dynamite will collapse the bridge. How do they all get across in time?
A: No throwing the flashlight back to the others. It’s too dark. The bridge will not hold three people. So two must cross together and then one must return with the flashlight to escort another across. The obvious choice is to send the two slowest together, but then does a slow man have to return with the light?
The solution is to send the two fastest men across first: 2 minutes elapsed. One returns with the light and it does not matter which one: say 2 minutes for a total of 4 minutes. Now the two slowest cross together: 10 minutes for a total of 14 minutes. The fastest returns with the light: 1 minute across, total 15. Finally the two fastest cross together again: 2 minutes and a total elapsed time of 17 minutes. The bridge blows, but they are on the other side just in time.
October
Q: There are three covered boxes. One contains diamonds. One contains rubies. The third box contains both diamonds and rubies. Each box is clearly labeled on the outside with its contents. Each label is wrong. You must close your eyes as you pick one gem from one of the boxes to examine. Now correctly determine what is in each box and keep the entire treasure.
A: Obviously you need to be certain that you learn some relevant information from the box you choose. Choose a gem from the box marked “Diamonds and Rubies”. You know that it is not from the “Diamonds and Rubies” box, since all the boxes are marked incorrectly. If you choose a diamond, then that box must contain only diamonds. Now since every box is labeled incorrectly, the “Rubies” can not be in the box marked “Rubies” of the remaining two boxes, so they must be in the box marked “Diamonds”. That leaves the box marked “Rubies” to contain the combination diamonds and rubies. Similar logic follows if you were to choose a ruby first. Enjoy your treasure!
September
Q: How can you cut, while making a straight-line cut, a rectangular piece of cake exactly in half after someone has already cut a rectangular piece out of it? There are two ways to do it.
A: Here are two solutions.
1. The one piece of information you need to know for the first solution is that if you draw a straight line at any angle through the center of a rectangle you will cut it exactly in half. So just determine the center of each rectangle and draw a straight line through the two center points. This line will divide the remaining cake in two equal pieces.
2. The second solution is easier but often overlooked. Simply cut the cake in half vertically. See drawing for both solutions.
August
Q: With a 3-quart bucket and a 5-quart bucket, measure exactly 4 quarts?
A: Here are two solutions.
1. Fill the 5-quart bucket and empty it into the 3-quart bucket until the 3-quart is exactly full, leaving you with 2 quarts in the 5-quart bucket. Empty the 3-quart bucket and pour the 2 quarts from the 5-quart bucket into it. Refill the 5-quart bucket to the top and then remove exactly one quart by pouring it into the remaining 1 quart space available in the 3-quart bucket. Now you have exactly 4 quarts in the 5-quart bucket.
2. Fill the 3-quart bucket and pour it into the 5-quart bucket. Refill the 3-quart bucket and then top off the 5-quart bucket with it to leave exactly 1 quart in the 3-quart bucket. Empty the 5-quart bucket and pour the 1 quart into it. Refill the 3-quart bucket and pour it into the 5-quart bucket to yield exactly 4 quarts.
Q: You have 8 baseballs. One of them weighs slightly less than the others. How do you find the “light” ball using a balance in just two weighings?
A: Choose any three baseballs and balance them against any three other baseballs. There are two possible outcomes.
1. If they balance equally, then one of the two baseballs not in the weighing is the light baseball. Simply balance the two remaining balls to determine which is the light baseball.
2. If they do not balance, you have reduced the possibilities to the three baseballs on the light side of the balance. Now choose any two from the light side. If they balance, it’s the one you didn’t choose from the light side. If they don’t balance, you have the light baseball on the light side of the scale.
