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## 7 Matchstick Equation Puzzles

In matchstick puzzles, you are presented with an incorrect equation made using matchsticks, and you must move 1 or more matchsticks to turn it into a valid equation.

You must use all of the matches, and you are not allowed to make an inequality symbol such as ≠, ≥, >, <, or ≤.

Try these 7 fun matchstick equation puzzles!

7 + 2 = 9

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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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## 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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## Zero-less Factors

What two numbers contain no zeroes and can be multiplied together to produce 100000?

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## How Many Friday the 13th in a Year

Some consider Friday the 13th (any Friday that falls on the 13th day of a month) unlucky.

In a calendar year, how many Friday the 13th can occur? Find both the minimum and maximum.

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## Consecutive Numbers Grid Puzzle

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:

1. Any two consecutive numbers must share a row/column (1 and 16 should be considered consecutive).
2. No row/column can contain three consecutive numbers.

Fill in the remaining numbers.

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## Matchstick Math 3

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!

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## I Like the Numbers 4 and 5

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 be written as the sum of 4’s and 5’s?

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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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## 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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## Matchstick Minimization 1

What is the smallest number you can make by moving exactly 2 matches above?

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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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## 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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## Calculator Error Riddle

A kid is adding consecutive integers on a calculator, one at a time, starting with 1 + 2 + 3 + … and so on. At one point you notice the sum is now 100, but that shouldn’t be possible if the kid was adding this way. The kid tells you that he made an error and subtracted exactly one of the numbers he was supposed to add.

What is the number he subtracted?

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## Eight Eights

Can you arrange eight eights so that the numbers add up to 1000?

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## Guess the Number

Jake has a 4-digit number in mind and asks Raj to guess the number. Raj can have 7 guesses, and Jake will give him some hints after 6 guesses.

Raj makes these 6 guesses:

• 6 3 5 8
• 9 3 0 6
• 4 8 8 2
• 6 7 2 8
• 1 1 9 1
• 5 6 2 7

These were all wrong, but Jake says every guess had exactly one (and only one) correct digit in the correct position. Additionally, all the digits are different.

What should Raj’s 7th guess be?

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## Confusing Zip Codes

The U.S. uses 5-digit zip codes to help determine where mail goes. Since mail can be oriented in all sorts of directions, they avoid assigning zip codes that could be confused with a different zip code when read upside-down. For example, 61666 could be confused with 99919 when upside-down, so mail could be accidentally routed to the wrong zip code if both were actual zip codes.

How many zip codes could be confused with a different zip code when read upside-down?

In the example above, 61666 and 99919 would count as two confusing zip codes. Also, zip codes are allowed to start with 0, such as 00501.

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## Analog Clock Puzzle

How many times do the hour and minute hands meet on an analog clock every day? What are those times?

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## Fix the Equation

Make the following line a valid equation using only these mathematical operators: addition, subtraction, multiplication, division, parentheses, exponentiation, square root, and factorial.

2 2 2 2 = 50

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## Four Digits Squared

Which perfect square of a 4-digit number has the same last four digits as the original number?

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## 24 Game Puzzle

How do you use 3, 3, 8, and 8 to make 24?

Each number must be used exactly once, and only addition, subtraction, multiplication, division, and parentheses can be used.

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## Match Maximization

What is the biggest number you can make by moving exactly 2 matches in the number above?

Assume that numbers must be represented in their standard “digital clock” font (for example, a “1” requires two segments).

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## A and B

A + B = A * B = A / B

What are the values of A and B?

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## Swap Digits

Swap two of the digits in this equation to make it a valid equation:

7 x 7 + 9 x 9 = 138

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## Missing Dollar Riddle

Three friends decide to split the cost of hiring a cleaner. The agency charges them \$30, so they each hand over a \$10 bill.

Later the agency discovers the rate was actually \$25 instead of \$30. They send the cleaner with \$5 to reimburse the friends.

It’s hard to split \$5 three ways, reasons the cleaner, so he gives the friends \$1 each, and keeps \$2 for himself as a tip.

But wait – each friend paid \$9, for a total of \$27, and the cleaner pocketed \$2. That’s 27 + 2 = 29, whereas they originally handed over \$30. Where did the missing dollar go?

The missing dollar riddle is a classic, well-known riddle of unclear origin – usually with a clerk and a room bill or a waiter and a restaurant bill. But it’s simple yet tricky, and may trip up even savvy puzzle-solvers.