Algebra Math Riddles Collection

A collection of Algebra Math Riddles for fun and pleasure! Tease your brain with these riddles, then check your answers.

Also visit our Math Trivia page for more arithmetic riddles, geometry riddles, statistics riddles, calculus riddles etc.

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Algebra Riddles

The Cat, Fish, And Bird Riddle
A child spent $100.00 to get 100 toy animals. The child bought at least one cat, one fish, and one bird, and did not buy any other toys. If a cat costs $10.00, a fish costs $3.00, and a bird costs $0.50, how many of each toy did the child buy?

The Lying Fishermen Riddle
Catherine asks,“How many fish did you catch?"
Barney said,“I caught 5."
Alfred said,“I caught 2."
Barney then says,“Don’t listen to Alfred. You have to multiply any number he speaks aloud by 6 to get the real value."
Alfred then says,“Don’t listen to Barney. You have to subtract 2 from any number he speaks aloud to get the real value."
Catherine knows Alfred always speaks aloud a number equal to the real number divided by some constant, and Barney always speaks aloud a number equal to the real number plus some fixed value.
Catherine, after thinking it over, says,“I know how many fish each of you actually caught!"
How many fish did Barney actually catch, and how many did Alfred actually catch?

Apple, Banana and Cherry Riddle
The numbers a, b, and c are positive integers.
An apple cost $a, a banana costs $b, and a cherry costs $c.
The cost of b apples, b bananas, and a + b cherries is $77.
What would the cost be for one apple, two bananas, and one cherry?

How would you prove that 2 = 1?

  • Show Answer

    If a = b (so I say)                                        [a = b]
    And we multiply both sides by a
    Then we’ll see that a2                                  [a2 = ab]
    When with ab compared
    Are the same. Remove b2. OK?                 [a2− b2 = ab − b2]

    Both sides we will factorize. See?
    Now each side contains a − b.                     [(a+b)(a − b) = b(a − b)]
    We’ll divide through by a
    Minus b and olé
    a + b = b. Oh whoopee!                                [a + b = b]

    But since I said a = b
    b + b = b you’ll agree?                                 [b + b = b]
    So if b = 1
    Then this sum I have done                          [1 + 1 = 1]
    Proves that 2 = 1. Q.E.D.

    Written by PeterW

    (Just in case you’re wondering - the above proof is incorrect because in step 5, we divided by (a - b) which is 0 since a = b)

Why didn’t the Romans find algebra challenging?

How can you add eight 8’s to get the number 1,000?

How do we know that the following fractions are in Europe? A/C, X/C and W/C ?

  • Show Answer

    Because their numerators are all over C’s.

Two fathers and two sons sat down to eat eggs for breakfast. They ate exactly three eggs, each person had an egg. How is that possible?

What digit is the least frequent between the numbers 1 and 1,000 (inclusive)?

  • Show Answer

    The digit 0. The other digits will have the numbers with repeated digits. For example, the digit 1 will have 11 and 111 but the digit 0 won’t have 00 or 000.

What digit is the most frequent between the numbers 1 and 1,000?

  • Show Answer

    The digit 1. This is because we are including the 1 from the number 1000.

What do you get when you combine Einstein and Pythagoras discoveries?

How do you expand (a + b)2?

  • Show Answer

    (a            +            b)           2

A man is in a tree and using a pot. What do you call the pot? (submitted by Matt)

Are these too easy? You may want to try some harder math puzzles or math riddles by Lewis Carroll

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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