Ask Dr. Math

Elementary Archive

Browse Elementary Puzzles
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to frequently posed puzzles:
    A hen and a half...
    Measuring with two containers.
    Heads, legs: how many animals?

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Eleven Sections of Fence [05/29/2003]

I have a grid containing 16 squares. Each square represents 1 acre. I need to draw 11 sections of fence along the dotted lines of the squares so that 4 fields are formed, each containing 4 acres of land.

Finding a Rule That Fits an Input-Output Problem [08/26/2006]

My daughter has an input-output chart problem where she has to find a rule and fill in the missing numbers. How can I help her with it?

Finding Input-Output Rules [10/08/2003]

My 3rd grader is having trouble finding rules to change one list of numbers (the inputs) into another (the outputs)...

Finding the Bad Machine by Gumball Weight [05/13/2008]

Nine gum ball machines produce gum balls that weigh 1 ounce, and one bad machine produces identical looking balls that weigh 0.5 ounce. With one weighing on a scale, determine which machine is defective.

Finding the Next Number in a Series [07/22/2002]

Are there any formal or systematic methods for solving problems that ask you to find the next number in a series?

Find Two Numbers [11/14/2001]

The sum of two numbers is 16 and their product is 48.

Four Twos Puzzle [05/31/1999]

How can I get 15, 17, 19 and 21 using 4 twos?

Fraction Puzzle Using Digits from 0 to 9 [02/04/2008]

Using all ten digits from 0 to 9 one time each, make five fractions that have values less than 1/2.

Fraction Riddle [09/05/2003]

How can 1/2 of 9 be 4?

Fun Brain Twister [8/22/1996]

Use six 7's to write an expression that has a value of 110.

A Game in Three Rounds [04/19/1999]

After three rounds each of the girls has 8 chips. How many chips did they have at the start?

Game of 24 [7/15/1996]

A student takes four numbers and combines them by addition, subtraction, multiplication, division, or a combination thereof to produce an answer of 24.

The Game of 24 [3/14/1995]

Using addition, subtraction, multiplication, and division, can you use 7,7,3,3 to make 24?

The Gift of the Magi [09/08/2002]

What mathematical error can be found in the first paragraph of O. Henry's 'The Gift of the Magi'?

Guess and Check - How Many Coins? [10/03/2002]

Jeremy has seven fewer coins than Hanna. If together they have 83 coins, how many coins does Hanna have?

Heads and Legs [07/25/2001]

Joe counts 48 heads and 134 legs among the chickens and dogs on his farm. How many dogs and how many chickens does he have?

How Does the Crystal Ball Know What Number I Chose? [01/05/2010]

Doctor Ian reveals how a mind-reading crystal ball "knows" the number you've chosen: represent any two-digit number 'ab' as 10*a + b....

How Does the Fido Puzzle Work? [05/12/2004]

Can you give me the mathematical explanation of how the Fido puzzle works? You can find the puzzle at http://digicc.com/fido/.

How Heavy is the Brick? [11/15/1997]

If a brick weighs a kilogram plus half a brick, how heavy is the brick?

How to Create a 4 x 4 Magic Square [01/28/2004]

Is there a general technique for creating a 4 x 4 magic square so that the rows, columns, diagonals, four center squares and four outside corner squares each add up to a desired number?

How to Make a Square with Three Lines [06/19/2001]

My teacher says it is possible to make a square with three lines, but I don't know how to do it. Can you help me?

I am 5 digits long... [12/16/1994]

... I am divisible by 3 and 9, but not 6; my digits add up to 27...

Jack & Jill Mind Teaser [8/29/1995]

If Jack had a 5 gal. bucket and Jill had 3 gal. bucket, and they each carried an equal amount to fill an 8 gal. bucket, how was this accomplished?

Kindergarten Math Problems [11/1/1994]

I am a kindergarten teacher who has some very interested and interesting math students. Are you willing to talk with us about math? Maybe you have a problem for us to work on so we can get acquainted?

Longest Roman Numeral [05/03/2007]

Which year in our recorded history has had the greatest number of Roman numerals in it?

Magic Triangle Sums [02/04/2003]

Find 6 consecutive odd numbers such that their magic triangle sum is 25. Find 6 consecutive numbers such their magic triangle sum is 4.

Making a Hard Square Sum Problem Easier [01/30/2004]

Given these eight numbers: 1/4, 1/2, 3/4, 1, 1 1/4, 1 1/2, 1 3/4, and 2, place three numbers along each side of a square so that the sum of the three numbers on each side of the square is equal to 3. Is there a trick to doing this kind of problem?

Making a Parallelogram [06/19/2001]

Make five shapes - a parallelogram, a square, and three triangles - into one parallelogram.

Making Change [04/15/1999]

What is the greatest amount of money John can have in his pocket?

Math Riddle [03/12/2001]

How do 5 and 9 more make 2?

Math Trick Question [02/02/2005]

How do I draw a square using only 3 lines?

Multiplying by 11 [09/16/1997]

We said: 568 x 11 and after about 5 seconds she said the answer was 6248. How did she do it so quickly?

Multi-Step Patterns [09/04/2003]

Find the rule that will give the second number if you know the first...

Number Puzzle: 26, 70 [09/12/2001]

The sum of two numbers is 26; 4 times the first number plus 2 times the second number equals 70. What are the two numbers?

Number Puzzle Based on Multiplication Ideas [08/07/2005]

Find the smallest possible natural number that ends in 6 such that if the 6 is erased and placed in front of the remaining digits, the resulting number is 4 times as large as the original number.

Number Puzzle with Digits 1-9 in a 3 by 3 Grid [10/09/2006]

In a 3 cell by 3 cell grid, use the digits 1 through 9 to fill in the cells so each horizontal, vertical, and diagonal row of three has a sum of 15. I've tried many possibilities with no luck!

Numbers on a Star Brain Teaser [01/03/2008]

Place the numbers 20, 21, 22, 23, 24, 25, 27, 28, 29 and 31 on a star so that each line of four numbers has a sum of 100. Each number can only be used once. Is there a way to do this besides guessing and checking?

One Billion as Product of Two Numbers with No Zeros [12/12/2001]

Write 1,000,000,000 as the product of two numbers, neither of which contains any zeros.

Order of Operations Problems - a General Strategy [10/23/2002]

Make equations using 7, 26, 46, and 15 to equal 160; 18, 9, 24, and 20 to equal 18.

Paper-Cutting Trick [01/24/2001]

Is there a way to cut a sheet of paper so as to make a hole big enough to walk through?

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