Ten Problems

1 B.C.
There were 129 years between the birth of Cleopatra and the death of Boadicea; but, as their united ages amounted to 100 years only, there must have been 29 years when neither existed-that is, between the death of Cleopatra and the birth of Boadicea. Therefore, Boadicea must have been born 29 years after the death of Cleopatra in 30 B.C., which would be in the year 1 B.C.

1113213211

Starting from the second line, each line describes the line above it. That is, the second line (11) describes the one 1 on the first line. The third line (21) describes the two 1s on the second line. The fourth line (1211) describes the one 2 and the one 1 on the third line.

So the line after 13112221 is 1113213211 - one 1, one three, two 1s, three 2s, one 1.

Bob’s horse is named Friday. He rode Friday to and from downtown.

The wording is misleading. The men were not supposed to have paid $30: they were supposed to have paid $25.

Look at it this way: The cash register contains $25 of the men’s money. The cashier has $2. The three men have the $3. That’s all there is to it.

Overall, the men paid $27, of which $2 went to the cashier’s pocket.

A gets 97 diamonds, C gets 1 diamond, and either D or E gets 2 diamonds.

This one is tough. Work backwards.

Say the thugs are named A, B, C, D and E, lined up in that order.

D and E know that if it comes down to the two of them (if A, B and C die), E will take all 100 diamonds. Even if D gives himself 1 diamond and E 99 diamonds, E can just vote against the idea, kill D, and take all the diamonds.
D 0 // E 100

C, knowing this, can choose to give himself 100 diamonds. He knows he has D’s vote, because D can’t risk going to the final vote, where E can simply vote to kill D no matter what.
C 100 // D 0 // E 0

B needs two votes from C, D and E. If he gives E 1 diamond, he knows E will vote for him, since otherwise C will give E none. He also needs to give 1 diamond to D, since D knows he will not have a chance to get any diamonds later. The remaining 98 diamonds, he gives to himself.
B 98 // C 0 // D 1 // E 1

A, knowing all of the above, needs two votes from B, C, D and E. Since C knows he can’t get any diamonds according to B’s plan, A can secure C’s vote by giving him 1 diamond. Then he can get the final vote he needs by giving either D or E 2 diamonds - more than they can get according to D’s plan. A can claim the remaining 97 diamonds.
A 97 // B 0 // C 1 // D 2 // E 0 (or D 0 // E 2)

Open the box labelled “mixed.” By looking at even one contained fruit, you can correctly re-label that box, since it cannot be mixed.

Scenario 1: The box labelled “mixed” contains apples. Then, the box labelled “apples” contains oranges and the box labelled “oranges” is mixed.
Scenario 2: The box labelled “mixed” contains oranges. Then, the box labelled “oranges” contains apples and the box labelled “apples” is mixed.

Turn on two lights. Leave them on for a while and turn one off. Remember which switch you left on, which switch you left off, and which switch you turned on but later turned off.

Go into the room. The light that is on corresponds to the switch you left on.

Feel the lights that are off. The one that feels hot corresponds to the switch you turned on then off. The one that feels cold corresponds to the switch you left off.

Light both ends of one stick, and one end of the other stick. As soon as the first one completely blows out (marking 30 minutes), light the unlit end of the other stick. The time the remaining stick blows out marks 45 minutes.

The paragraph does not contain the letter e anywhere. This is a very unusual feat, since e is the most common letter of the alphabet and the most difficult to “avoid.” In fact, the book Gadsby written by E. V. Wright contains about 50000 words with no e anywhere.

Possible answers are 991 and 987654321.