Larry Campbell Brain Teasers

May/June ’16 Brain Teasers

  1. A palindrome is a number, like 535, that reads the same forward or backward.  How many palindromes are there between 10 & 1000?
  2. A cheetah was clocked running 550 feet in 10 seconds.  How many miles per hour is that?
  3. The sum of A & B is 112.  If A is 4 more than C, and B is 2 less than C, what does C equal?
  4. Name two consecutive prime numbers whose product is 899.
  5. If you omit the digit common to both numerator and denominator of 26/65, you don’t change its value, because 26/65 = 2/5.  There are several fractions with that weird trait.  Can you find at least one more? (As always, a simple ‘yes’ or ‘no’ will not get full credit. :-)).
  6. Find the first place where there are three (3) consecutive integers which are all composite (not prime & not 0 or 1). [BONUS:  Can you do the same for 4?  5?  Any number?]
  7. Which of these is the biggest (largest in value) fraction?  3/7, 4/9, 2/5
  8.  True or False:  A)  If the sum of two numbers is even, then both numbers are even.  B)  If the product of two numbers is even, then both numbers are even. C) A number with 5 factors is always bigger than another number with 4 factors.
  9. True or False:  I can’t seem to format the question parts in #8 so that they will number and indent correctly.
  10. Every day from June 10 to June 19 this month was a palindrome!  (Reading the same front and back, disregarding punctuation – see also BT#1).  E.g. June 16:  6/16/16.  Cool!!  For this BT, A)  When did such a string last occur, if ever?  B)  When will it next occur, if ever?
  11. Alice won’t take part in the play if Betty is in it!  But Charles will only participate if Alice is in it.  The producer insists that one of the girls be in the play, and two people are needed total.  Who is in the play?
  12. Find positive integers a, b, c such that 1/a + 1/b + 1/c = 1.

16 thoughts on “May/June ’16 Brain Teasers”

  1. Larry,
    #1 palindrome – do you mean between 100 and 1000? If you do mean 10 to 1000, are you expecting us to write 10 as 010, 20 as 020, etc?

    1. Good question/clarification, Jim, but no. Just look at them as written. 20 does not need to be written as 020 (any more than 220 needs to be written 0220). So, without giving too much away, 20 is not a palindrome, but 22 is.

  3. Can the numbers be run together as 101112131415 or only separate as 10 11 12 13 14 15?

    1. Hi Dan!!
      I THINK you’re referring to Question 1 about palindromes? Good question, but I’m not quite sure how to answer it.
      Do you mean could the ‘new number’ be considered a palindrome? Well yes (if it read same both ways), but that wouldn’t have much to do with the ‘original’ numbers, and whether or not they are palindromes.
      Does that help any?? If not, feel free to follow up.
      Larry

  4. 1. 99 total – 9 two-digit and 90 three-digit palindromes
    2. 37.5 miles/hour
    3. A = 59, B = 53, C = 55 (I love systems of equations! 🙂
    4. 29 & 31
    5. (saving for another time)
    6. 8, 9 , and 10

  5. 1. 99 numbers
    3. C=55
    8. All are False
    9. True! I hate when I can’t get it to do what I want!

  6. #5 Yes I can find one more example with the weird trait described in the question.
    #11 The answer is Betty and a fourth person named Pat. Alice and Charles are not picked because they are being so difficult about casting the play.

    1. Thanks, Jim – As always, typically ‘creative’ answers. 🙂 Since they won’t really help anyone too much with answers, I’ll go ahead and post/approve this now.
      As to #5, I don’t doubt your veracity, of course, but as it says in the BT, a yes/no answer won’t get you full credit. 🙂
      And your answer to #11, while not sticking to the probably-intended hypotheses, WILL in fact work. If others want to agree with Jim here, I’ll need to give you credit, as well.

      1. Larry,
        In #5 it is specifically stated that a “simple” yes or no will not receive credit. My answer was not a simple yes and therefore within the parameters set within the question and should receive credit.
        jdw

        1. Ah, Jim . . . always enjoy ‘sparring’ with your mind. 🙂 The court notes your opinion for the record, but objection overruled anyway.
          Being somewhat of a literalist myself, I thought you might be thinking that. But it appears we’ll be quibbling over the meaning of ‘simple’ here. Your answer simply reaffirmed/repeated your ‘yes’ with a sentence re-stating the same thing. Hence, it’s still a ‘simple’ yes answer. (As opposed to an answer of ONLY yes or no.) To go beyond ‘simple’ requires an explanation.
          Have you seen ‘Princess Bride’? They actually cut part of the scene where he says ‘never get into a land war in Asia’ . . the next line was ‘never get into a wording battle with another literalist: neither of you will be satisfied.’
          Have a good one!! Larry

  7. Larry,
    Yes. The explanation is this: there are a finite number of fractions that meet the given form and a systematic examination of those fractions will eventually reveal at least one fraction that meets the desired outcome. The desired form is ab/ca or ab/bc and the desired outcome is ab/ca=b/c or ab/bc=a/c, all fractions are less than one.
    It is immediately obvious that a, b, and c do not equal 0 because numbers are not written 0a, 0b, or 0c and fractions with a denominator of 0 is nonsensical in this brain teaser.
    Also, a may not be larger than 4 or the numerators may not be larger than 49 because all denominators will have 3 digits.
    I found 19 fractions that meet the form and 3 of those meet the desired outcome.

  9. #6 14, 15, 26
    25, 26 27, 28
    32, 33, 34, 35. 36
    #7. 3/7=135/315; 4/9=140/315; 126/315 Answer is 4/9
    #8 A False, B false, C false
    #9 True, it SEEMS that you cannot format Question 8 in the manner described in the question 9.
    #11 If limited to the 3 and assuming the producer is a wimp and caves into the demands of Alice and Charles, the answer is Alice and Charles.
    #12 1/2 + 1/3 + 1/6 = 12/24 + 8/24 + 4/24 = 24/24 = 1

  10. Larry,
    Yes. The explanation is this: There are a finite number of fractions that meet the given form and a systematic analysis of those fractions will eventually reveal at least one fraction that meets the desired outcome. The candidate fractions have 2 digit numerators and 2 digit denominators where the numerator is a factor of the denominator, the fractions are equal to a number less than one, and can be characterized as ab/ca or ab/bc. The desired outcome is ab/ca = b/c or ab/bc = a/c.
    It is immediately obvious that a, b, and c do not equal 0 because numbers are not written as 0a, 0b, or 0c and a 0 in the denominator is nonsensical in this brain teaser.
    Further the numerator of the candidate fractions may not be larger that 49 because if the numerator is 51 or higher the denominator will have a 3 digit number and that disqualifies it for the brain teaser.
    Additionally, the numerator must be larger than 10 and less than 50. That leaves only 36 numerators to be examined.
    Furthermore, all denominators must be greater than the companion numerator. The larger the numerator the fewer acceptable denominators there will be . As it turns out there are only 100 fractions to be examined.
    Once the 100 fractions have been identified the next step is to look for the desired form of the fractions to create a final list of candidate fractions; again the desired form is ab/bc or ab/ca. There are 20 (?) fractions that meet that form.
    Among the 20 there are 4 that meet the desired outcome, one of which is found in the question..
    jdw

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