All but Two
A man describes his daughters, saying, “They are all blonde but two; all brunette but two; and all redheaded but two.” How many daughters does the man have?
SOLUTION
The man has 3 daughters; one blonde, one brunette, and one redhead.
Category: Brain Teasers
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12 Balls, 1 Defective
You have 12 balls, 11 of which have the same weight. The remaining one is defective and either heavier or lighter than the rest. You can use a balance scale to compare weights in order to find which is the defective ball and whether it is heavier or lighter. How many measurement do you need so that will be surely able to do it?
SOLUTION
It is easy to see that if we have more than 9 balls, we need at least 3 measurements. We will prove that 3 measurements are enough for 12 balls.
We place 4 balls on each side of the scale. Let balls 1, 2, 3, 4 be on the right side, and balls 5, 6, 7, 8 on the left side.
CASE 1. The scale does not tip to any side. For the second measurement we place on the left side balls 1, 2, 3, 9 and on the right side balls 4, 5, 10, 11.
If the scale again does not tip to any side, then the defective ball is number 12 and we can check whether it is heavier or lighter with our last measurement.
If the scale tips to the left side, then either the defective ball is number 9 and is heavier, or it is number 10/11 and is lighter. We measure up balls 10 and 11 against each other and if one of them is lighter than the other, then it is the defective one. If they have the same weight, then ball 9 is the defective one.
If the scale tips to the right side, the procedure is similar.
CASE 2. Let the scale tip to the left side during the first measurement. This means that either one of the balls 1, 2, 3, 4 is defective and it is heavier, or one of the balls 5, 6, 7, 8 is defective and it is lighter. Clearly, balls 9, 10, 11, 12 are all genuine. Next we place balls 1, 2, 5, 6 on one side and balls 3, 7, 9, 10 on the other side.
If the scale tips to the left, then either one of the balls 1, 2 is defective and it is heavier, or ball 8 is defective and lighter. We just measure up balls 1 and 2 against each other and find out which among the three is the defective one.
If the scale tips to the right, the procedure is similar.
If the scale does not tip to any side, then either the defective ball is 4 and it is heavier, or the defective ball is 8 and it is lighter. We just measure up balls 1 and 4 against each other and easily find the defective ball.
Not Twins
A teacher enters the classroom and sees on the first row two students sitting next to each other, looking completely identical. She asks them if they are twins, but the students simultaneously reply that they are not. After checking in the records, the teacher furthermore discovers that the two children have the same mother and father. What is the explanation?
SOLUTION
The students are three of a triplet.
Shape Encoding
Based on the logic of the first four pairs of words and shapes, figure out what the fifth word is.
SOLUTION
The first letter is P if the shapes are circles and B if the shapes are squares.
The second letter is A if the shapes are green and E if the shapes are red.
The third letter is N if the number of shapes is 2 and R if the number of shapes is 3.
The fourth letter is T if the shapes are arranged vertically and S if the shapes are arranged horizontally.
Therefore, the last word should be BENT.
Easy Money
The horse got $18, the the bee got $27, the duck got $9, and the spider got $36. How much did the snake get?
SOLUTION
Every animal got $4.50 for every leg it has. Therefore, the snake got nothing.
Isometric Puzzles
There is a 3D body embedded inside a 3×3 cube. For each of the six puzzles below, recreate the body based on the views from the top, the front, and the right.
SOLUTION
The solutions are shown below.
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Gerrymandering
The city has 49 districts that vote for blue, yellow, or purple as shown in the grid. Seven electoral regions are drawn up to elect a city council. Each region consists of seven districts and each region will elect one councilor. Can you gerrymander the map so that blue will win the majority?
SOLUTION
The solution is shown below.
US Presidents
The 22nd and 24th presidents of the United States of America had the same parents but were not brothers. How can this be possible?
SOLUTION
They were the same person, Grover Cleveland.
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Family Issues
Her father went to prison, her mother mortgaged all her properties and her brother sold his house, but she couldn’t be happier. Why?
SOLUTION
Because they were playing Monopoly.
Birthday Twins
Darma and Greg are twins, Greg being the older one by just few moments. However, several times in their lives, Darma celebrated her Birthday two days before Greg did. How is this possible?
SOLUTION
Darma and Greg were being delivered on a plane/ship which was passing the 180th meridian. This way Greg got born on 1st of March and Darma got born on 28th of February. Therefore, during leap years, Darma will celebrate her Birthday 2 days before Greg.