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 twodigit 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 horsetrading 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 eightdigit 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 twodigit 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 bullseye, 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 fourdigit 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 fourdigit 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 15minute 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 SeongChang 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 onedigit 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.
