Common Thread

What do the following words have in common?

• dust
• seed
• left
• resign
• weather
• sanction

Click below to see the answer.

Each word has at least two meanings, and in each case one of those meanings is the opposite of the other.

• dust - as a verb can mean either to add or remove something.
• seed - also means either to add or remove something. If you seed the lawn you add seeds, but if you seed a tomato you remove them.
• left - can mean either remaining or departed.
• resign - can mean "to quit" but can also mean "to sign up again."
• weather - can mean "to withstand or make through" (weather the storm) or can mean "to be worn away."
• sanction - can mean 'give official permission or approval for (an action)' or conversely, 'impose a penalty on.'

For these and more, see the Mental Floss article 25 Words That Are Their Own Opposites.

Marking a Ruler

A 13-inch ruler only needs four markings on it so that it can be used to measure any whole number of inches from 1 to 13. At what positions should the four markings be? (Do not include the two ends, which are understood to be markings 0 and 13.) Click below to see the answer.

The markings should be at the 1, 2, 6, and 10-inch positions. Use the following markings to measure each whole-number length:

1 inch: 0 to 1
2 inches: 0 to 2
3 inches: 10 to 13
4 inches: 2 to 6
5 inches: 1 to 6
6 inches: 0 to 6
7 inches: 6 to 13
8 inches: 2 to 10
9 inches: 1 to 10
10 inches: 0 to 10
11 inches: 2 to 13
12 inches: 1 to 13
13 inches: 0 to 13

Move One Digit

The following equation is incorrect. Can you make the equation balanced by moving only a single digit?

101 - 102 = 1

Click below to see the answer.

The digit that needs to be moved is the 2. Just move it up into the exponent and the equation is correct.

101 - 10² = 1

What is the next number in the sequence?

Without Googling it, can you tell me the next number in the following sequence?

1
11
21
1211
111221
312211
13112221
1113213211

That should be enough to see the pattern, but this sequence goes on infinitely. Click below to see the answer.

This sequence is known as the "Look and Say" or "Say What You see" sequence. Each term is formed by describing the previous term. The first term is just the digit 1. To describe it you would say "one one," so the next term is 11. To describe that you'd say "two one," and so on. The next term after the ones shown is 31131211131221. Check the Online Encyclopedia of Integer Sequences (A005150) for more terms following that.

Beer Run

A man runs n laps around a circular track with a radius of t miles. He says he will drink s quarts of beer for every mile he runs. How many quarts will he drink? Click below for the answer.

He will only need one quart, no matter how far he runs. If the radius of the track is t miles, then the circumference is 2*pi*t miles. The man will run n laps, so the total distance is 2*pi*n*t miles. If he drinks s quarts per mile, then the total amount of beer is 2*pi*n*t*s, which equals one quart!