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Mathematics Tricks Puzzles

20 Mathematics Trick Puzzles

Puzzle 1: Multiply any number by 9

Pick any number, multiply it by 9, then add the digits of the result. What do you always get?

Answer: You always get 9!

Puzzle 2: Double and halve

Pick any number, double it, then halve it. What will the result be?

Answer: The result is always the original number!

Puzzle 3: 1089 Trick

Think of a 3-digit number where the first and last digits differ by at least 2. Reverse the digits and subtract the smaller number from the larger. Reverse the result and add. What is the final answer?

Answer: The final result is always 1089!

Puzzle 4: Multiply by 11

Take any 2-digit number and add the digits together. Place the sum between the original digits. What is the result?

Answer: The result is the original number multiplied by 11!

Puzzle 5: Sum of first 100 numbers

What is the sum of the first 100 positive integers?

Answer: 5050 (Using the formula n(n+1)/2)

Puzzle 6: The magic of 1

What do you get when you multiply 111,111,111 by 111,111,111?

Answer: 12,345,678,987,654,321

Puzzle 7: Multiply by 25

How can you quickly multiply any number by 25?

Answer: Divide by 4 and multiply by 100!

Puzzle 8: Magic number 37

Pick a multiple of 3, multiply it by 37. What do you notice?

Answer: The result will be a repeating pattern (e.g., 3 * 37 = 111, 6 * 37 = 222, etc.)

Puzzle 9: Divisibility rule for 9

How can you quickly tell if a number is divisible by 9?

Answer: If the sum of the digits is divisible by 9, so is the number!

Puzzle 10: Square any number ending in 5

How can you easily square any number ending in 5?

Answer: Multiply the first digit(s) by itself plus one, then append 25 (e.g., 35² = 3 * 4 = 12, so 35² = 1225)

Puzzle 11: Multiplying by 4 and 5

What’s an easy way to multiply a number by 45?

Answer: Multiply by 9 and then by 5!

Puzzle 12: Multiply by 99

How do you multiply any number by 99 quickly?

Answer: Multiply by 100 and subtract the original number!

Puzzle 13: Divide by 5

What is a fast trick to divide any number by 5?

Answer: Multiply by 2, then divide by 10!

Puzzle 14: Sum of consecutive integers

What is the sum of 1 + 2 + 3 + ... + 99?

Answer: 4950

Puzzle 15: Find any square root

How do you estimate the square root of any number?

Answer: Find the nearest perfect squares, then use them to approximate.

Puzzle 16: The 9 pattern

Multiply any number by 9, then add the digits of the product. Keep adding until you get a single digit. What is it?

Answer: Always 9!

Puzzle 17: Rule of 11 divisibility

How can you tell if a number is divisible by 11?

Answer: Alternately subtract and add the digits. If the result is divisible by 11, so is the number.

Puzzle 18: Multiplying even numbers

What’s the shortcut for multiplying any even number by 5?

Answer: Halve the number and multiply by 10!

Puzzle 19: Sum of angles in a polygon

How do you find the sum of the interior angles of any polygon?

Answer: (n-2) * 180, where n is the number of sides!

Puzzle 20: Any number to the power of zero

What is any number raised to the power of zero?

Answer: Always 1!

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