Brain Teasers and Puzzles

Brain teasers, puzzles, riddles, and other challenges

Ferry Boat Problem

Two ferry boats serve the same route on a river, but travel at different speeds. They depart from opposite ends of the river at the same time, meeting at a point 720 yards from the nearest shore.

When each boat reaches the other side, it takes 10 minutes to unload and load passengers, then begins the return trip. This time, the boats meet at a point 400 yards from the other shore.

How wide is the river?

The ferry boat problem is created by well-known puzzle author Sam Loyd.

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Converge to an Integer

Given the iterative formula:

xn+1 = sqrt(xn) + a

There are some values of a for which a positive starting value for x results in this formula converging to an integer.

For example, if a = 2, you would observe that xn+1 = sqrt(xn) + 2 eventually converges to 4 for any positive starting value.

What form must a take in order for this formula to converge to an integer?

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Finish My Wordle

These Wordle puzzles are nearly complete, you just need to finish them by figuring out the correct word. In each of these 5 puzzles, there should be just one or two valid answers remaining – find them!

Haven’t played Wordle before? You get 6 tries to guess the 5-letter English word, and for each guess you are shown whether each letter is in the right place in the word (green), in the word but in the wrong place (yellow), or not in the word at all (gray).

Wordle 1
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Russian Roulette Riddle

In the morbid game of Russian Roulette, a partially loaded revolver with a six-chamber cylinder is randomly spun, pointed at one of the players, and fired. If the revolver landed on an empty chamber, the lucky player is safe, and the process is repeated with the next player. The obvious objective of the game is to not get shot.

You find yourself stuck in a game of Russian Roulette. A freshly loaded revolver is aimed at the first player, and it turns out to be an empty chamber. Your turn is next, and you are given the choice to either:

  • Spin the cylinder before pulling the trigger (i.e., you get a random new chamber)
  • Or just pull the trigger (i.e., let the revolver fire whatever is in the next chamber)

Which choice should you pick if the revolver was originally:

  1. Loaded with one bullet?
  2. Loaded with bullets in two random chambers?
  3. Loaded with bullets in two consecutive chambers?

Assume the revolver cannot misfire, and that spinning the cylinder lands on all chambers with equal probability.

Some variation of this Russian Roulette riddle was once asked in interviews at Jane Street, Susquehanna International Group (SIG), Facebook (now Meta), UBS, Capital One, and more.

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