Additional Investigations

Consecutive Primes: Investigate sums and averages of two consecutive primes.

Perfect Numbers: Find perfect numbers.

Six Divisors: Find the divisors of the number N.

Nonrepeating Decimals: Examine the relationship between the denominator and the numerator in fractions with nonrepeating decimal representations.

How Old are Three Daughters?: Help a census taker figure out a father's riddle about his daughters' ages.

Cutting Hair: Determine how long a hair cutter works on a busy day.

Don't Just Say "It's Undefined": Consider division by 0 and 1.

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

Divisibility by Eight: Explore a possible rule for checking divisibility by eight.

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

Abundant Numbers: Find abundant numbers.

Abundant Numbers II: Determine if Sam's claim about abundant numbers is true.

Abundant Numbers III: Examine abundant numbers.

Abundant, Deficient, and Perfect: Find patterns among abundant, deficient, and perfect numbers.

Mental Squaring: Square two-digit numbers in your head.

Odd and Strange: Discover some strange properties about a mysterious number.

Sum of Consecutive Integers: Use the sum of consecutive integers to form certain numbers.

Counting the Years: Using personally significant dates, you can find a surprising result.

Summing Away: Find the sum of consecutive integers.

Take a Different Base: Determine numbers in different bases.

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

Constructing Triangles: Construct triangles with particular attributes.

The Differences Between Horses and People: You know how many legs and heads are in a crowd. Now determine how many horses are there.

Pick up the Sticks: Devise a strategy so that you're the one leaving the last stick on the table every time.

Caging Mice: Put a different number of mice in each cage.

Happy Numbers: Find happy numbers and patterns among them.

Irrational to Rational: Use square roots to produce integers.

Making Change: Find different ways to make change for a dollar.

The Last Digit: Determine the last digit in a huge number.

Square Root Patterns: Find the square root of a huge number.

Sums and Products: Using sums and products, what's the largest number less than 50 that you cannot produce?

Perfect Square Columns: Find the perfect squares in a given table.

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

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

Can You Get 100?: Manipulate digits to get a sum of 100.

Cryptorithms: Translate letters into numbers.

Those Numbers Below: Consider the use of the word "below" for negative numbers.

Calendar Math: Will the sum of four numbers always be the same?

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

Magic Hexagon: Make the sum of each of the rows equal certain numbers.

Magic Circle: Make the sum of all rows equal the same number.

Paying for Lunch: What happened to the other dollar?

The Horse Problem: How much does a man make or lose in the horse-trading business?

Measuring Exact Amounts: Can you produce exactly 3 gallons of water?

Forgetful Fran: Help Fran remember how much money she loaned each friend.

Squaring and Cubing: Find numbers that are either squares or cubes.

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

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

Perplexing Properties: Find a number with these special properties.

Consecutive Products: Find consecutive numbers whose product is a particular number.

Extended Pythagoras: Find three special numbers that add up to 365.

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.

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

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

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

How Many Thousands?: Find possible values of a digit in an eight-digit number when you know one of its divisors.

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

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.

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

Who Wants to Win One Million?: Find particular factors that produce 1,000,000.

Ending a Perfect Square: Find a special number that can make other numbers into perfect squares.

Difference of Squares: Write a given number as the difference of two squares.

What number is it?: Determine a number given its particular properties.

The End Digits: What are the last two digits of a huge number?

The End Digits II: What are the last two digits of large power of 7?

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

One's Digit: Determine the one's digit of a large number.

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?

Powers of Three: Express a given number as a power of 3.

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

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

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.

Ready Fire Aim!: If three darts are thrown at a bulls-eye, what are the possible totals?

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

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

Carnival Fun: Determine if Amelia won the panda.

Turning Red: At what time will two traffic lights turn red together?

Dollars and Sense: In how many ways can you make change for a dollar using certain coins?

Tallying an Election: Determine the number of votes a particular candidate could have received.

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

Magic Square: Place the numbers in the diagram's squares in a special way to create a magic square.

Remainder Shells: How many shells does Ken have in his shell collection?

Products and Sums: Find a decimal number that meets certain requirements.

The Secret Pocket: How many of each kind of coin does Keith have in his secret pocket?

Unknown Ages: If Roberto was born on his grandmother's birthday, how old are Roberto and his grandmother now?

Finding Palindromes: How many four-digit palindromes exist?

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

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

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

Know Your ABCs: Determine the product of abc under certain restrictions.

Aging Adults: If you know the product of two adults' ages, can you determine the age of the younger adult?

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?

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

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

Squares inside Squares: Find the four-digit number that fits the description.

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

Integer Function: Find the smallest integer for which an expression results in an integer.

Family Math: How old are a mother and son?

Going to the Movies: How many children and adults attended a special matinee of a magic show?

Multiple Dozens: Write the largest multiple of 12 given certain restrictions.

Factor Five: Examine numbers with exactly five factors.

Nails in a Pail: Determine how much a pail and nails weigh.

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

Boxes in Boxes: Determine how many boxes are empty.

Missing Numbers: Find the numbers represented by each letter in the puzzle.

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?

Heavy Reader: How many pages did Alexis read?

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

Factoring Days: Is today's date a factor of this month?

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

Counting Zeros: Determine the number of zeros at the end of a particular factorial.

Counterfeit Coin: Find the counterfeit coin.

Judy's Gift: How much money did Judy give Dave?

Prime Factor Sums: Find numbers whose prime factors equal a certain sum.

Siblings: How old are the twins and their younger brother?

Nonconsecutive Grid: Arrange the numbers in a 4x4 grid under a certain condition.

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

Summing Evens: Find a way to sum a set of even integers.

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

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

Magic Pairs: How many pairs of "magic" numbers exist?

Filling Bases: Find the missing base numbers.

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

Coat Check: How many times will Allison write the digit 3?

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

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

Submit your idea for an investigation to InterMath.