Three problems with one arrangement that fits. More logic riddles are in the logic drawer.
Three closed boxes. Exactly one note is true. Box 1 says the prize is in this box. Box 2 says the prize is not in this box. Box 3 says the prize is not in box 1. Where is the prize?
If two notes can be true at once, that arrangement is out.
Answer. Box 2.
Prize in box 1 makes notes 1 and 2 true. Prize in box 3 makes notes 2 and 3 true. Prize in box 2 makes only note 3 true.
Three jars: pencils, erasers, or both. Every label is wrong. You may draw one item from one jar. Which jar, and how do you name the rest?
The only jar whose wrong label you can test with one draw is the one that claims to be mixed.
Answer. Open the jar labeled both.
It cannot be mixed, so it is pure. If you draw a pencil, that jar is pencils. The jar labeled erasers is not erasers and not pencils, so it is both. The last jar is erasers.
1, 11, 21, 1211, 111221, ?
Read each term out loud as a description of the term before it.
Answer. 312211
Each line describes the previous line. 111221 is one 1, one 2, two 1s. The next line says three 1s, two 2s, one 1.