## 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…

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…

Find a combination of three different positive integers x, y, and z such that: x3 + y3 = z4 Hint: there’s a better way than brute force / trial & error.

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…

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…

White to play and mate in 4.

Quick vocabulary puzzle – given the middle four letters of each word, figure out these 8-letter words:

13 10 4 16 7 The cells in this 4×4 grid puzzle contain the numbers 1-16 each once. There are two rules to the arrangement of the numbers: Any two consecutive numbers must share a row/column (1 and 16 should…

This puzzle was coined the “Impossible Puzzle” by Martin Gardner, a famous math and science writer that liked to create and write about math games and puzzles. The puzzle is named as such because it appears to provide insufficient information…

Form four lines of four coins by moving exactly 3 of the coins below: Rules: Coins cannot be stacked on top of one another. A line of five or more coins is still only considered one line. The centers of…

Rearrange exactly 2 matches to make this a valid equation. In matchstick math puzzles, you are not allowed to make an inequality symbol such as ≠, ≥, >, <, or ≤. That would make it too easy!

A truel is a three-way duel. The three participants take turns firing one shot at whichever opponent they choose, until only one is remaining. Allison, Ben, and Chase are in a truel, and have varying degrees of accuracy: Allison has…

White to play and mate in 3.

What common word or phrase is this rebus referring to? NAFISHNAFISH

Suppose there is a game in which you roll a fair, 6-sided die and win dollars equal to the outcome of the roll. How much would you expect to win on average? Suppose, if you don’t like the outcome of…

Quant interview question often contain brain teasers involving mathematics, statistics, and logic. The goal of these questions is to assess your quantitative and reasoning abilities, which can be highly relevant to working as a quant analyst, trader, or developer. Here…

I like the numbers 4 and 5. I like to add 4’s and 5’s together to make other numbers, such as 4 + 4 + 5 + 5 + 5 = 23. How many numbers from 1 to 1000 can…

On a magical island, there are 100 lions and 1 sheep, all of which can live by eating the plentiful grass on the island. Any lion that eats the sheep will magically turn into a sheep afterward, such that there…

Brain teaser interview questions were quite common in tech, finance, and consulting interviews for a period of time. Here are 7 brain teaser interview questions and answers encountered in actual interviews, including engineering interviews at Apple and Microsoft – how…

Remove 6 matches from the diagram above to leave two squares, with no extra matches lying around.

White to play and mate in 6. This one is very tough!

A man wants to enter an exclusive club, but doesn’t know the password. He observes a few other patrons: Thinking he has figured it out, the man walks up and the doorman says “10”. The man replies “5” but it’s…

These words all have an unusual property in common, what is it?

A man is throwing rocks off a boat floating in the middle of a lake. The rocks sink quickly to the bottom of the lake. Does the water level in the lake rise, fall, or stay the same after the…

In some cultures, it is typical for guests at an event to shake hands when they meet other guests (when there isn’t a pandemic). Some might be more social and shake hands with a lot of other guests, while others…

Move exactly 1 match to make this a valid equation. In matchstick math puzzles, you are not allowed to make an inequality symbol such as ≠, ≥, >, <, or ≤. That would make it too easy!