A puzzle by Sam Loyd:

Here is a pretty problem which I figured out during a ride from Bixley to Quixley astride a razor-back mule. I asked Don Pedro, a native guide who walked ahead of me pulling the mule forward by its reins, if my steed had another gait. He said it had but that it was much slower, so I pursued my journey at uniform speed. To encourage Don Pedro, who was my chief propelling power, I said we would pass through Pixley, so as to get some liquid refreshments; and from that moment he could think of nothing but Pixley.

After we had been traveling for forty minutes I asked how far we had gone. Don Pedro replied: ‘Just half as far as it is to Pixley.’

After creeping along for seven miles more I asked: ‘How far is it to Quixley?’ He replied as before: ‘Just half as far as it is to Pixley.’

We arrived at Quixley in another hour, which induces me to ask you to determine the distance from Bixley to Quixley.

A puzzle by Emily Cox and Henry Rathvon, from the October 1991 issue of Games magazine:

You’re visiting a familiar island on which each resident either invariably lies or invariably tells the truth. Three residents appear.

Resident 1: We’re all liars.
Resident 2: Just one of us is a truth teller.

The third resident doesn’t speak. Which of the three are telling the truth?

In 1882, Lewis Carroll invented a game he called MischMash:

The essence of this game consists in one player proposing a ‘nucleus’ (i.e., a set of two or more letters, such as GP, EMO, IMSE), and in the other trying to find a ‘lawful word’ (i.e., a word known in ordinary society and not a proper name), containing it. Thus, ‘maGPie,’ ‘lEMOn,’ and ‘hIMSElf’ are lawful words containing the nuclei GP, EMO, and IMSE.

He sent these nuclei to his godson. What English words contain these fragments?

OLS
VY
NGU
EWH
STEN

From the Strand, December 1903: These tracks were left by a man in flight leading a child. “In order to throw his pursuers off the trail the man changed his means of locomotion at each of the places marked in numbers on the diagram. The problem consists in discovering the manner of locomotion between each of these stations and the next; what vehicles the man took; what happened to him in the course of his flight; and what he did with the child at the different stages of the journey.”

A puzzle by A. Khalamaizer: Move three of these circles to make the triangle point downward.

I don’t know who devised this; I found it in The Batsford Chess Puzzle Book (2002). Black has only a king and a bishop, while White still has all 16 of his men. But Black threatens to take White’s knight, giving mate immediately. If each side uses every legal expedient, what will be the outcome? For a start, White can stave off mate with 1. Bh2!

What word has kst in the middle, and at the end, and in at the beginning?

Five pirates of different ages want to divide a treasure of 100 gold coins. They agree that the oldest among them will propose how to divide the coins, and then all the pirates will vote on the proposal. If more than half the pirates support it, it will be adopted and the coins distributed accordingly. Otherwise the proposer will be thrown overboard and the process repeated with the remaining pirates.

If all five pirates are smart, rational, greedy, and fearful of death, what will happen?

I have 13 magnetic tapes on reels; one empty reel; and a machine that can unwind a tape from a full reel onto an empty one, reversing the tape’s direction. I need to reverse the direction of each tape while leaving it on its original reel. Can this be done?

This logic puzzle is the numerical equivalent of a crossword. Each white cell in the diagram is to be filled with a digit from the range 1-9. The sum of each string of digits must match the “clue” given in the diagram. For example, the clue 29 above means that the four digits to its right must sum to that total. No digit may be duplicated within any entry. Can you complete the diagram?