Brain Easer
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Brainteasers, puzzles, and other thought-provoking content carefully curated to hone your analytical skills, prepare for interviews and expand your knowledge.
Brain Easer
10M ago
Honkai: Star Rail features a number of interesting logic puzzles in its quests. One side quest has you questioning suspects to determine the detector thief. Similar to some classic “who is lying” logic puzzles that you might have encountered before!
Here is the Honkai Star Rail detector thief puzzle, and how to solve it:
Who is the detector thief?
You interrogate the four suspects, and each makes one claim:
Cook says the helper did it
Tailor says it wasn’t her
Merchant says the cook did it
Helper says it wasn’t him
Swetta also tells you a critical piece of information: only one of the suspe ..read more
Brain Easer
11M ago
If you have me, you want to share me. If you share me, you haven’t got me. What am I?
Click to show solution to “If you share me you haven’t got me”
A secret
Many people who have a secret want to share it. But if you share a secret, it is no longer secret, so you haven’t got it anymore ..read more
Brain Easer
11M ago
A detective is called upon to solve the riddle of the mystery killer in a high-profile murder.
There are only three suspects:
Aaron, the best friend
Patty, the gardener
Jason, the neighbor
The victim was holding a calendar, and it seems he marked several of dates before he passed away: the second of January, the sixth of February, the third of April, the fourth of October, and the first of November.
With this information, the detective identified the culprit. Who was it?
Click to See Solution to Mystery Killer Riddle
Aaron
The calendar was marked such that each day refers to the position of ..read more
Brain Easer
1y ago
In a certain classroom, 75% of the students can speak English, 55% of the students can speak French, and 10% speak neither language.
What percentage of the students speak both languages?
Click to reveal solution
40%
You can think of the whole group of students as comprising the 75% of students that speak English, the 55% of students that speak French, minus the x% of students that speak both languages (because this group has already been counted twice, we subtract to avoid double-counting), plus the 10% the speak neither:
100 = 75 + 55 – x + 10
Solving this equation gives us x = 40 ..read more
Brain Easer
1y ago
The Monty Hall Problem
You are on a game show in which there are three identical doors, one with a car behind it and two with goats behind them. You must pick one door, and you win if that door has the car behind it.
After you pick a door, the host of the game show always opens a door you didn’t choose that has a goat behind it. This leaves the door you chose and one other remaining door, and you are given the option to switch your choice to the other remaining door.
Should you switch or should you stick to your original choice? What chance of winning would that give you?
The History
The Monty ..read more
Brain Easer
1y ago
Move exactly 2 matches to make this a valid equation.
Bonus: find two different solutions.
In matchstick equation puzzles, you are not allowed to make an inequality symbol such as ≠, ≥, >, <, or ≤. That would make it too easy!
Solution
9 – 1= 8
or
2 + 7 = 9 ..read more
Brain Easer
1y ago
White to play and mate in 2.
Solution
Qh3
If 1. … Rxh3, then 2. Rxh3#
If 1. … Nxh3 or Ne2, then 2. Rf1#
If 1. … Nxf3, then 2. Qf1 ..read more
Brain Easer
1y ago
If a triangle has two sides with lengths 3 and 4, what should the length of the third side be in order to maximize the area of the triangle?
Solution
5
Using Calculus
This is the type of problem that calculus was designed to solve:
If a triangle has side lengths a and b, and the angle between them is θ, then the area of the triangle is ab sinθ
To find the maximum, find the value of θ such that the derivative of the area is equal to zero: (ab sinθ)’ = ab cosθ = 0
There are multiple solutions, but only 90° is a valid solution for an angle of a triangle – therefore it’s a right triangle and the ..read more
Brain Easer
1y ago
Compound words are words that are composed of two or more other words, like high + light = highlight.
Can you make compound words out of the following three words by adding the same 4-letter word either before or after each word?
CROSS
WORKS
WILD
Solution
Add “FIRE”:
CROSSFIRE
FIREWORKS
WILDFIRE ..read more
Brain Easer
1y ago
Prove that for all prime numbers p > 3, (p2 – 1) is a multiple of 24.
Solution
First, factor the expression: p2 – 1 = (p + 1) (p – 1)
Among any 3 consecutive numbers, one must be a multiple of 3. Since p is a prime number greater than 3, p is not a multiple of 3. Therefore, either p + 1 or p – 1 must be a multiple of 3, which means (p + 1) (p – 1) is a multiple of 3.
Since p is a prime number greater than 3, p is odd and both p + 1 and p – 1 must be even. Among any two consecutive even numbers, one must be a multiple of 4 and the other must be a multiple of 2. Therefore (p + 1) (p – 1) is ..read more