Multiple Calculations

Place the digits 1 through 9 in the empty boxes in a special way.

Common Digit

Find the one-digit number that is just like all the others.

Coat Check

How many times will Allison write the digit 3?

Apples and Oranges

They say you cannot add apples and oranges. You do in this puzzle! Can you break the code?

Filling Bases

Find the missing base numbers.

Magic Pairs

How many pairs of “magic” numbers exist?

Clocking the Order

When will the digits of a digital clock be in strictly increasing order? In strictly decreasing order?

Train Tracking

Follow the pattern and determine the number of people who get on and off the train.

Summing Evens

Find a way to sum a set of even integers.

On Target

How many darts will Seong-Chang need to throw to earn a specific number of points?

Nonconsecutive Grid

Arrange the numbers in a 4×4 grid under a certain condition.


How old are the twins and their younger brother?

Prime Factor Sums

Find numbers whose prime factors equal a certain sum.

Judy’s Gift

How much money did Judy give Dave?

Counterfeit Coin

Find the counterfeit coin.

Counting Zeros

Determine the number of zeros at the end of a particular factorial.

Cooking an Egg

How could you cook eggs for 15 minutes if you do not have a 15-minute timer?

Factoring Days

Is today’s date a factor of this month?

Dividing Primes

Which numbers are divisible by all three of the smallest prime numbers?

Heavy Reader

How many pages did Alexis read?

Using up Digits

Can you find a multiplication sentence using the digits 1, 2, 3, 4, 5, and 6 such that the product is closest to a certain number?

Missing Numbers

Find the numbers represented by each letter in the puzzle.

Boxes in Boxes

Determine how many boxes are empty.

Calendar Math

When does the product of the month number times the day number equal the last two digits of the year?

Nails in a Pail

Determine how much a pail and nails weigh.

Factor Five

Examine numbers with exactly five factors.

Multiple Dozens

Write the largest multiple of 12 given certain restrictions.

Going to the Movies

How many children and adults attended a special matinee of a magic show?

Family Math

How old are a mother and son?

Integer Function

Find the smallest integer for which an expression results in an integer.

Seven Envy

Use the same whole number and the operations +, -, x, and ÷ to produce a certain number.

Squares inside Squares

Find the four-digit number that fits the description.

Impossible Scores

What is the highest score below 100 that is impossible to score on a given dart board?

Five Alive

If you wrote a list of consecutive whole numbers, how many times would you write the digit 5?

Multiple Digits

Betty wrote a list of consecutive whole numbers starting with the number 1. If you know how many digits she used, can you determine the last number Betty wrote?

Aging Adults

If you know the product of two adults’ ages, can you determine the age of the younger adult?

Know Your ABC’s

Determine the product of abc under certain restrictions.

Sharing Cookies

In how many ways could Moe, Larry, and Curly share eight cookies?

Even Factors

Examine numbers whose factors are all even, except for the number 1.

Five Divisors

Use the digits 1, 2, 3, 4, and 5 to make a number that fits the description.

Finding Palindromes

How many four-digit palindromes exist?

Unknown Ages

If Roberto was born on his grandmother’s birthday, how old are Roberto and his grandmother now?

The Secret Pocket

How many of each kind of coin does Keith have in his secret pocket?

Products and Sums

Find a decimal number that meets certain requirements.

Remainder Shells

How many shells does Ken have in his shell collection?

Magic Square

Place the numbers in the diagram’s squares in a special way to create a magic square.

Aiming for Combinations

Annie shoots three arrows that all land inside rings of an archery target. What were her three scores?

Tallying an Election

Determine the number of votes a particular candidate could have received.

Dollars and Sense

In how many ways can you make change for a dollar using certain coins?

Turning Red

At what time will two traffic lights turn red together?

Carnival Fun

Determine if Amelia won the panda.

Spending Wisely

What is the largest number of video games a customer can purchase?

Dividing by a Set

Find the least positive whole number that is divisible by all the numbers in a particular set.

Ready Fire Aim!

If three darts are thrown at a bulls-eye, what are the possible totals?

How Did We Do?

In a mathematics contest find out how many of your team’s answers were incorrect and how many problems were unanswered.

Ordering Chocolate

How many boxes are needed to fill an order for 1256 chocolates?

Trouble Sleeping

Determine when the Johnson triplets will go to sleep at the same time.

Powers of Three

Express a given number as a power of 3.

Reversing Digits

Can you find a two-digit number that gives a particular sum when the original number and the number obtained by reversing its digits are added?

One’s Digit

Determine the one’s digit of a large number.

Magic Triangle

Place the digits 1 through 9 in the circles in a very special way.

The End Digits II

What are the last two digits of large power of 7?

The End Digits

What are the last two digits of a huge number?

What Number Is It?

Determine a number given its particular properties.

Difference of Squares

Write a given number as the difference of two squares.

Ending a Perfect Square

Find a special number that can make other numbers into perfect squares.

Who Wants to Win One Million?

Find particular factors that produce 1,000,000.

Fortune Telling

Using only a digit and the four basic operations (+, -, x, /), produce a set of numbers.

Inside a Domain

Find all the whole numbers that can replace the variable x in a given expression so that the expression has a particular value.

100 Sums

Do any numbers from a given set have a sum of 100?

How Many Thousands?

Find possible values of a digit in an eight-digit number when you know one of its divisors.

Situational Reminders

Find the smallest positive integer when you know its divisors and remainders.

Mystery Number

Given three of its twelve factors, what is the mystery number?


Find a sequence of calculator key presses that produces a given number in the display.

Multiple Ages

Determine my age given that it is a multiple of a particular integer one year and a multiple of a different integer the next year.

Extended Pythagoras

Find three special numbers that add up to 365.

Consecutive Products

Find consecutive numbers whose product is a particular number.

Perplexing Properties

Find a number with these special properties.

Adding Places

Determine how many times the digits of each number less than 209 add to 8.

Balancing Entertainment

Help Jasmine determine how many CDs, tapes, and videos she can buy.

Squaring and Cubing

Find numbers that are either squares or cubes.

Forgetful Fran

Help Fran remember how much money she loaned each friend.

Measuring Exact Amounts

Can you produce exactly 3 gallons of water? 

The Horse Problem

How much does a man make or lose in the horse-trading business?

Paying for Lunch

What happened to the other dollar?

Magic Circle

Make the sum of all rows equal the same number.

Magic Hexagon

Make the sum of each of the rows equal certain numbers.  In the hexagons below, place the numbers 1-19 so that rows, columns and diagonals all add up to 38. (Source: Eric W. Weisstein) Extension: Place the numbers 1-19 in the circles so the sum of each of the rows with three circles around the […]

Magic Square

Make the sum of the numbers in the rows, columns, and diagonals of a grid all equal the same integer. 

Calendar Math

Will the sum of four numbers always be the same?

Those Numbers Below

Consider the use of the word “below” for negative numbers.


Translate letters into numbers.

Can You Get to 100?

Manipulate digits to get a sum of 100. 

Multiples of Places

Find a number with a special relationship between two of its digits.

Composite Numbers

Follow the steps in manipulating a number and be surprised by the result!

Perfect Square Columns

Find the perfect squares in a given table.

Sums and Products

Using sums and products, what’s the largest number less than 50 that you cannot produce? 

Square Root Patterns

Find the square root of a huge number.

The Last Digit

Determine the last digit in a huge number.

Making Change

Find different ways to make change for a dollar.

Irrational to Rational

Use square roots to produce integers.

Happy Numbers

Find happy numbers and patterns among them.

Caging Mice

Put a different number of mice in each cage.

Pick Up the Sticks

Devise a strategy so that you’re the one leaving the last stick on the table every time. 

The Differences Between Horses and People

You know how many legs and heads are in a crowd. Now determine how many horses are there.

Constructing Triangles

Construct triangles with particular attributes.

Relationships in the Hundreds

Find numbers in the hundreds with a special relationship among the digits.

Take a Different Base

Determine numbers in different bases.

Summing Away

Find the sum of consecutive integers.

Counting the Years

Using personally significant dates, you can find a surprising result.

Sum of Consecutive Integers

Use the sum of consecutive integers to form certain numbers. 

Odd and Strange

Discover some strange properties about a mysterious number.

Mental Squaring

Square two-digit numbers in your head. 

Abundant, Deficient, and Perfect

Find patterns among abundant, deficient, and perfect numbers. 

Abundant Numbers III

Examine abundant numbers.

Abundant Numbers II

Determine if Sam’s claim about abundant numbers is true.

Abundant Numbers

Find abundant numbers. 

Locker Counting

Which locker doors will be open when a given process is complete?

Divisibility by Eight

Explore a possible rule for checking divisibility by eight.

Multiples of Nine

Find a relationship pertaining to the digits in a multiple of 9.

Don’t Just Say “It’s Undefined”

Consider division by 0 and 1.

Cutting Hair

Determine how long a hair cutter works on a busy day.

How Old are Three Daughters?

Help a census taker figure out a father’s riddle about his daughters’ ages.

Non Repeating Decimals

Examine the relationship between the denominator and the numerator in fractions with non repeating decimal representations.

Six Divisors

Find the divisors of the number N.

Perfect Numbers

Find perfect numbers.

Consecutive Primes

Investigate sums and averages of two consecutive primes.