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## Matchstick Equation 4

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!

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## Mate in 2 Chess Puzzle 3

White to play and mate in 2.

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## Maximize Triangle Area

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?

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## Compound Word Puzzle 3

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
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## Most Frequent Digit

What is the most frequent digit among the numbers between 1 and 1000 (inclusive)? Consider only base-10 whole numbers.

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## Reroll the Die

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 the roll, you can reroll the die once, and win dollars equal to the outcome of the 2nd roll (once you choose to reroll, you can no longer go back to the 1st roll). How much would you expect to win on average?

Suppose, if you don’t like the outcome of the 2nd roll, you can reroll the die once more, and win dollars equal to the outcome of the 3rd roll (once you choose to reroll, you can no longer go back to previous rolls). How much would you expect to win on average?

This was an actual brain teaser question once asked at Jane Street for an interview for an intern role.

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## Leave Two Squares

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

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A man wants to enter an exclusive club, but doesn’t know the password. He observes a few other patrons:

• First patron walks up and the doorman just says “12”. The patron replies “6” and is let in.
• Second patron walks up and the doorman says “6”. The patron replies “3” and is let in.

Thinking he has figured it out, the man walks up and the doorman says “10”. The man replies “5” but it’s incorrect and he is turned away.

What should the man have said instead?

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## Something in Common

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

• Glory
• Knot
• Empty
• Hint
• Begin
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## Matchstick Math 2

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!

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## Compound Word Puzzle 2

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 to each of them?

• SHINE
• HONEY
• WALK
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## Compound Word Puzzle 1

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 to each of them?

• WOOD
• FALL
• SURF
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## Reverse the Digits and Add

I am thinking of a 3-digit number. When you reverse the digits of this number, you get a bigger number, and if you add that to the original number, the sum is 463. What was the number I was thinking of?

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## Drink Mix Riddle

Two kids are playing around with their drinks at lunch. One has 200ml of milk and the other has 200ml of chocolate milk. They scoop 20ml of chocolate milk into the milk glass, then they scoop 20ml of whatever is in the milk glass into the chocolate milk glass.

When they’re done, is there more chocolate milk in the milk glass or more milk in the chocolate milk glass?

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## Number Deduction

A teacher gives three clever students in her class a challenge: she writes down 3 different numbers on 3 index cards, and has each student hold up one of the cards to their forehead such that they can’t see their own card but everyone else can.

She tells them each card has a different number, and that two of the numbers add up to the third number, and asks them to figure out their number without sharing the numbers they see.

Ava says “I don’t know my number.”

Vlad says “I don’t know my number.”

Before Sid can say anything, Ava realizes she is now able to figure our her number! What is Ava’s number?

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## Matchstick Math 1

Move exactly 1 match to make this a valid equation.

Bonus: find two different ways to solve this.

In matchstick math puzzles, you are not allowed to make an inequality symbol such as ≠, ≥, >, <, or ≤. That would make it too easy!

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## Pulley Puzzle

In the pulley puzzle diagram below, there is a pulley attached to a scale. One side of the pulley is attached to a weight and the other side is attached to the ground.

If the scale reads 100g, does the weight weigh 50g, 100g, or 200g?

Assume the pulley and rope has no weight (the scale is already adjusted to account for these), and that the whole system is in equilibrium (nothing is moving).

Note: this puzzle is best solved with a bit of basic physics knowledge, but there is also an intuitive solution, so give it a shot.

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## Four-Card Problem

You see four cards with A, D, 3, and 6 face-up. You know that each card has a letter on one side and a number on the other side.

You are told that cards with a vowel on one side must have an even number on the other side. Which cards do you need to turn over to test if this rule is broken?

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## Rebus Puzzle 12

What common word or phrase is this rebus referring to?

NOONGOOD

Good afternoon

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## Trailing Zeros

How many trailing zeros does 1000! have?

“!” is the factorial symbol. For example, 12! = 12 x 11 x 10 x … x 2 x 1 = 479001600, which has 2 trailing zeros (zeros at the end of the number).

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## Rebus Puzzle 11

What common word or phrase is this rebus referring to?

LANG4UAGE

#### Solution

Foreign language (“four in language”)

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## Rebus Puzzle 10

What common word or phrase is this rebus referring to?

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## Who is Lying?

Chris says both Amy and Brad are lying.

Who is lying? Who is telling the truth?

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## One Move Each Chess Puzzle

White to play and mate in 3 – but white’s pieces must make exactly one move each!

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## Random Turns

You are in a city with streets on a perfect grid – every street is north-south or east-west. You are are driving north, and decide to randomly turn left or right with equal probability at the next 10 intersections.

After these 10 random turns, what is the probability you are still driving north?