Integer Additional

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

How many times will Allison write the digit 3?

Find the missing base numbers.

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

Find a way to sum a set of even integers.

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

Find numbers whose prime factors equal a certain sum.

Find the counterfeit coin.

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

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

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?

Determine how many boxes are empty.

Determine how much a pail and nails weigh.

Write the largest multiple of 12 given certain restrictions.

How old are a mother and son?

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

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

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?

Determine the product of abc under certain restrictions.

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

How many four-digit palindromes exist?

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

How many shells does Ken have in his shell collection?

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

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

Determine if Amelia won the panda.

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

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

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

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?

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

What are the last two digits of a huge number?

Write a given number as the difference of two squares.

Find particular factors that produce 1,000,000.

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

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

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

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.

Find consecutive numbers whose product is a particular number.

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

Find numbers that are either squares or cubes.

Can you produce exactly 3 gallons of water? 

What happened to the other dollar?

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 […]

Will the sum of four numbers always be the same?

Translate letters into numbers.

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

Find the perfect squares in a given table.

Find the square root of a huge number.

Find different ways to make change for a dollar.

Find happy numbers and patterns among them.

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

Construct triangles with particular attributes.

Determine numbers in different bases.

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

Discover some strange properties about a mysterious number.

Find patterns among abundant, deficient, and perfect numbers. 

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

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

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

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

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

Find perfect numbers.