Can you solve this math riddle?

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Daffy Duck waitingThree women friends went on a vacation in the Caribbean. To save money, they would share a hotel room.
The daily rate for the hotel room is $300.
Each woman paid $100, making up the $300.
But the hotel manager decided to give the women a discount and charged only $250 for the room. He told a clerk to return $50 to the three women.
The clerk pocketed $20 for himself, and gave the remaining $30 back to the three women.
Each woman got $10 back. Therefore, each woman actually paid $90 (100-10) to the hotel.
$90 x 3 = $270
$270 + the clerk’s $20 = $290
But the women originally gave the hotel $300.

Question: Where did the remaining $10 go?


Scroll down for the solution!


arrow2arrow2You’re stumped because you’ve been misled by how the question was posed to you.
Instead of looking at it as the three ladies actually paying $270, plus the $20 pocketed by the hotel clerk, thus equaling $290, which means $10 are uncounted for, the correct way to look at it is to start with the facts that we’ve been told:

  • Fact #1: Each woman initially paid $100 each.
  • Fact #2: Each woman got $10 back.
  • That means each woman actually paid $90 each.
  • In other words, altogether the women paid the hotel $270, not $300.
  • Fact #3: The hotel only charged them for and kept $250.
  • Fact #4: The hotel clerk stole $20.
  • $20 + $250 = $270.
  • There never was any “remaining $10”!

Another way to look at it is to look at what happened to the $300 that the 3 women originally paid the hotel:

  • Hotel kept $250.
  • Clerk stole $20.
  • Women got $30 back.
  • 250+20+30 = $300.
  • Once again, there’s no “remaining $10”!


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0 responses to “Can you solve this math riddle?

  1. It took me a few minutes, but I knew it was not really 300, but had to figure off of the 270.. yea me. 😀

    • Tell you what, I failed HS Math, and never did repeat it before graduation. Yet when I wrote the BC Dept of Labour Trade Qualification Test in Carpentry [3.0 hrs long!], I passed the first tie. Only 1 in 3 does, as it’s the MOST difficult in Canada, and w/the highest ‘Fail’ mark [I think 80%]. But I missed this one!

  2. but i’ve been to 57 states said obama.

  3. Once There was an Arab man with three sons.
    Upon his death his will was read.
    His oldest son was to recieve half of his father’s camels
    The middle son was to recieve 1 third of his camels.
    The youngest son was to recieve 1 ninth of his camels.
    The man left the three sons 17 camels to divide in these proportions.
    Alsa, the sons could not come up with a way to divide the camels as their father wished.
    So they went to their father’s oldest and wisest friend and explained their delimma to him.
    The old friend said to the sons “your father was my nearest and dearest friend. I have many camels and would be glad to give you one so that your father’s request can be satisfied.”
    Overjoyed the sons returned home with the additonal camel and proceeded to diviy up their inheratence.
    The oldest son took 1 half or 9 of the camels.
    The middle son 1 third or 6 of the camels.
    And the youngest son took 1 ninth or 2 of the camels.
    Since 9 + 6 + 2 = 17 they returned the remaining camel to their father’s old friend.
    Does anyone out there have the solution to this one? I sure don’t.

    • Laserboy,
      The original version of this math puzzle is as follows:
      A man owned 17 camels. When the man died he left behind 3 sons. In his will he bequeathed that his property should be divided as follows: Half (1/2) his property to his eldest son; One-third (1/3) his property to his second son; One-ninth (1/9) his property to his youngest son.
      The sons were in a quandary wondering how to divide 17 camels into respective shares of 1/2, 1/3, and 1/9 parts, which would work out to be:
      8.5 camels for the eldest son; 5.67 camels for the second son; 1.89 camels to the youngest son.
      Now how was it possible to divide camels in this manner? So they took their 17 camels and went to a Wise Man for advice.
      The wise man said: “No problem. It can be done. Add my camel to your 17 camels and now you tell me how many camels do you have?”
      “17 + 1 = 18. We now have 18 camels,” the sons said.
      The wise man looked at the eldest son and said: “Your share is half of the total camels – half of 18 works out to be 9 – so take your 9 camels and go away.”
      18 – 9 = 9. Now only 9 camels remained.
      Then the wise man looked at the second son and said: “Your share is 1/3 of the total camels – one third of 18 works out to be 6 – so take your 6 camels and leave.”
      9 – 6 = 3. Now only 3 camels remained.
      The wise man looked at the youngest son and said: “Your share is 1/9 of the total camels – one ninth of 18 works out to be 2 – so take your two camels and leave.”
      3 – 2 = 1. Now only one camel remained.
      This was the Wise Man’s camel. The Wise Man took his camel and walked home, having successfully divided the 17 camels amongst the 3 sons as decreed in their father’s will.

      Looked at in this way, son #1 got 9 camels, son #2 got 6 camels; son #3 got 2 camels = 17 camels. The wise man gets his one camel back = total of 18 camels!


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