Logic Puzzles

Popular Mechanics Logic Puzzles

Logic puzzles are an excellent way to challenge and engage players. They can be used to set a scene in which an intelligent character challenges one to a game of wits, or as a trap, or as a means of setting a locked gate that can only be opened by demonstrating one's intelligence.

Harder puzzles might be best reserved for time in between sessions - to allow the players time to think about the puzzle without stalling story momentum during gametime.

Seven Candles

Problem¹⁾
One night, as you are up reading an old book on your porch overlooking the Pacific, a great winged and tentacled creature emerges from the dark waters and seizes you. Its octopus arms drag you down into the hideous depths.

When you awaken you are surprised to be alive, and doubly surprised to find yourself in a small room with a circular table in the center. Water seeps through the walls. You get the sense that you are deep underwater, and only some unseen mystical barrier prevents a torrent of water from gushing into the room.

On the table are seven lit candles in a circle. You hear a deep voice echoing in your mind. It tells you that you must extinguish all seven candles, and should you fail to do so, you will never leave. When you blow out one candle in the circle, the two adjacent candles are extinguished as well. If you blow on a candle that has already been extinguished, it will relight. And if there is an extinguished candle next to the one you blow on, it also will relight.

To put it another way: When you blow on a candle, it—as well as the candles on either side—will change from lit to unlit, or vice versa.

How do you extinguish all seven candles? What is the least number of moves you can take to extinguish them all?

Hint
Blowing on the same candle twice is essentially the same as not blowing on it at all. Blowing on the same candle three times is the same as blowing on it once.

The Unfair Coin

Problem²⁾
Imagine you have an unfair coin, one that does not land on each side 50 percent of the time. How could you use this coin to simulate the 50/50 odds of a fair coin flip? Note: The coin does have heads on one side, and tails on the other. The probability of landing on either side is greater than zero. The coin will never land on its edge.

Hint #1
It does not matter how biased the coin is or which side it lands on more often. The solution remains the same regardless of the odds of one coin flip.

Hint #2
You are allowed to flip the coin more than once to simulate a 50/50 coin flip.

¹⁾

There is no reason to blow on the same candle more than once. As the hint points out, blowing on the same candle twice is the same as not blowing on it at all, and three times is the same as once. With this in mind, if you start blowing on each candle one at a time, ignoring the effect on other candles, you will quickly realize that that is the solution: blow on each candle once. You can go in order, from the first candle you blow on around the circle, and by the time you blow on the seventh candle all of the candles will be extinguished. You can also blow on the candles in any order you want, so long as you blow on each one once, and by the time you are done all of the candles will be extinguished. This is the minimum number of moves you can make to extinguish all the candles: seven. Congratulations, you extinguished the candles of the Old Ones, and Cthulhu was forced to let you go free… for now.

²⁾

Regardless of which side the coin lands on more often, and what the non-zero probability is that it will land on that side, one thing is always true for an unfair coin. If you flip it twice, the probability that you will get heads and then tails is the same as the probability that you will get tails and then heads. In other words, if heads is probability a and tails is probability b, then getting heads followed by tails would be a x b and getting tails followed by heads would be b x a, which are equal. So you either call HT or TH, and when you flip the coin twice you have four possibilities: HT, TH, HH, and TT. If you get heads twice or tails twice, you simply flip the coin two more times until you get one before the other. Which will occur first, HT or TH, is a 50/50 split, regardless of how unfair the coin is.

Amaranthum

Table of Contents

Logic Puzzles

Seven Candles

The Unfair Coin