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Assorted math and logic problems

Questioning is the basis of all learning.

  • Logic problems
    • Halloween - Which witch?
    • Poll problem age of children
    • Riddle of the Sphinx
    • First number with the letter A
    • People names in common
  • Geometry & visual spatial relationships -
    • Circles
    • Angel
    • Area Directions
    • Drink cups & best deal
  • Algebra & patterns
  • Pet care
  • Infinity
  • FUnctions
  • Exponents
  • What is your reason
  • Number value & operations
    • Addition & subtraction
    • Division
    • Division by zero
    • Multiplication 12345678987654321
    • Digit
    • Card contest


Logic and math

Halloween problem

Which witch?

Wilhelmina, Winifred and Wisteria are all witches. Winifred keeps a bat as a pet. Wilhelmina has a broomstick. Wisteria has a black cape and is 300 years old. The witch who can fly is 200 years older that Wisteria. The witch who owns a pet is half as old as is Wilhelmina.

Questions to answer:

  1. What is the combined age of the witches?
  2. Which witch is oldest?
  3. What does Wisteria own?
  4. How many years will it be before Wllhelmia is 600 years old?
  5. How old will Winifred be in the year 2000?
  6. If Wilhelmina ages only half as fast as Winifred, and Wisteria
    ages twice as fast, what will be the combined ages of the
    witches in the year 2100?

Source with more math mysteries


Poll Problem



  • Find all the factors for 36
  • Find eight sets of three with a product of 36
  • Find the sums of the eight sets
  • If the sum is a unique, you will know the answer
  • If it is not, then more information is needed.
  • If the older isn't a twin, then you should have it.

Riddle of the Sphinx

What walks on all fours in the morning, on two legs in the afternoon, and on three at night? OH! And if you answer incorrectly the Sphinx will eat you.

First number with the letter A

If you were to spell out numbers, how far would you have to count until you would find the letter "A"? ......

All the same

What do these people all have in common?

  1. Alexander the Great
  2. Attila the Hun
  3. Smokey the Bear

Geometry and visual spatial reasoning

Circle Problems

If you hold a quarter stationary and roll a dime around the perimeter of the quarter, how many revolutions will the dime make?

If a circle has a circumference of three and a smaller circle of circumference one roles around the larger one how many revolutions will it make?


What is the sum of all the vertex angles in a triangle?

What is the sum of all the vertex angles in a square?

What is the sum of all the vertex angles in a pentagon?

Pentagon with inscribed triangles

Find the area of floor plan

Floor plan to find area


A person leaves home makes three left turns, arrives back home, sees two masked people, and knows he/she is safe and feels great.

Who are the masked people?

Drink cups

Hot drink cups at one store come in four sizes:

Approximately what are the dimensions for each cup size?

Select inches or centimeters and design some cups. Describe how your design will almost be filled with the appropriate amount.



Pet care and sequences

Your neighbor family is going on a vacation for thirty days and ask you take care of their family pet. Since the family pet is very valuable they are concerned it gets very good care. They explain this to you and ask which method of payment you would prefer.

  1. $10, 000 a day for each day they are gone and the pet lives.
  2. $.01 the first day, $.02 the second day, $.04 the third day, $.08 the fourth day and so on for each day the pet lives.

You are not concerned about the pet dying, since you will take very good care of it. Assuming the pet lives all thirty days which plan will you take to make the most money?


Why is .999999... equal to 1?

Explain to the student who says.

"Shouldn't it be equal to .0000000000 ... 1? I mean if you compare the two there should be a difference of one somethingth. Shouldn't there be?"


If you have the function 2n + 1
What is n?

What do you want it to be?
It is a function, it can be whatever you want it to be.

Try some numbers ...
Like, 0, 1, 2, 3, 4,

If you do you get the set ...
1, 3, 5, 7, 9...

Are they infinite?

How can the set of whole numbers and the function 2n + 1, set both be infinite? It woul seem that one-half the other ...

Consider the function, 2x + 1. (Note: other letters could be used instead of x, like n ...)

When this function turns up in the world it usually represents odd numbers.

What about a function for x squared?

What about a function for x squared and z squared?

Are they always squares?


If 32 is 3*3 = 9 or three time three two times, then shouldn't 30 be three times three zero times or zero.

What's your reason?

1. There are 100 centimeters in a meter. So support or reject 100 cm = m as a valid or invalid statement?

Number value and basic operations

Addition & subtraction

Three and Five bucket problem

A person has a three and five liters bucket and needs to measure four liters. How can it be done?






A person wants to put 14 cookies on a plate and has 169 cookies. How many plates can be filled? or How many 14's are in 169? Represent the problem with diagrams. One with plates and another with one hundred square, ten rods, and one cubes.

Division by zero

If 6 / 2 = 3 because six cookies divided onto two plates means there is three cookies on each plate.

Therefore 3 / 0 would be three divided onto zero plates would be ...?

What two numbers can be multiplied to get 12,345,678,987,654,321?

111,111,111 x 111,111,111


Subtract nine digits which total 45 from nine digits that also total 45 and have a difference of nine digits which also has a total of 45.

Card Contest

A collector can win a contest for 100 baseball cards if she/he can solve this problem. She/he will be given $100.00 to purchase 100 cards if she/he can figure how to select cards from three groups so that the total for 100 cards will be exactly $100.00. The cards must be selected from only three groups which costs are: $.50 group one, $3.00 group two, and $10.00 group three. How many from each group can be bought and what is each group's total cost?