Chuck Grimmett

Day 40 – Math Problem

When I was in South Haven, I went to a used book store and bought a “Mathematical Games” book. It had all kinds of neat math games to play with shapes and simple everyday objects such as matches. There were riddles in the back of the book and one intrigued me. Let’s see if the people who read my blog can get it:

“A stranger walked into the local sweet shop and bought chocolates for six shillings. He paid with a ten-shilling note, which they could not change, and so the shopkeeper went next door to the tobacconist, who was able to change the note for him. The shopkeeper returned with the change, gave the four shillings change to the stranger, who then left. The tobacconist returned the next day with the note, which turned out to be counterfeit. The owner of the sweet shop was obliged to give him his ten shillings back. How much did the sweet shop lose altogether? Explain.”

It is not a trick question, there is a solution. Give your answer and provide support. I will post the answer in a few days in the comments.

My day today was wonderful.  I got up at 7 a.m. and went to the sports complex to exercise, took a shower, then had time for breakfast before class. It felt great! I was awake and had lots of energy without drinking caffeine. I plan on doing that a few days a week. I expect to have more energy overall and sleep better (that is what people say exercising does for you). Also, it was a wonderful day outside here and people are cheerful because of it. It was overall just a pleasant day today.

Chuck Grimmett

Posted by Chuck Grimmett. Learn more on his About page.

Comments

10 responses to “Day 40 – Math Problem”

  1. Ted Avatar
    Ted

    Twenty shillings. The ten he refunded the tobacconist, the four he gave the stranger in change, and six for the chocolates.

    Reply
  2. Robert Lajdziak Avatar
    Robert Lajdziak

    The shopkeeper loses 10 shillings. he gives the 10 shilling note to the tobacconist and the tobacconist gives him lets say 10 single shillings. then he gives the four shillings change to the customer. since the customer gave him the fake bill the tobacconist wants his money back, so the sweetshop man gives him the six shillings the guy paid with plus four more to make it to 10 shillings. If he didn’t have to pay the ten shillings meaning the tobacconist didn’t find out he wouldn’t have lost anything,because he made a trade with the customer. if it was an even trade than the cost of chocolate was exactly 6 shillings assuming the sweetshop owner didn’t make a profit. I originally thought 14, but I’m sure it is 10 because he didn’t lose the money that he gave to the customer, he traded him.

    Reply
  3. Dad Avatar
    Dad

    I am with Ted! 20

    Reply
  4. Steve Stay Avatar
    Steve Stay

    I’m voting for 20 shillings, too. The customer gave the sweetshop owner a fake bill, so no money was exchanged there. The sweetshop owner at first gained 10 shillings from the tobacconist. He gave six shillings-worth of candy and four actual shillings to the customer (=10), then gave another 10 shillings to the tobacconist, totaling twenty.

    Reply
  5. Mort Avatar
    Mort

    Assume: actual worth of item is 6.
    Now, realize that the tobacconist is extraneous information. How can I say that? Well, he has no net gain or loss. He might as well be the cash register. Forget him. He gives money, then he gets the same amount.
    For that matter, it doesn’t matter that the person gives the conman a box of chocolates and 4 shillings. Just say he gives him 10 shillings.
    That puts the situation this way: the seller gave the conman 10 shillings, while the conman gave the owner nothing.
    Net Loss = 10 shillings
    Ta Da!

    Reply
  6. Nonarchist Avatar
    Nonarchist

    10 shillings. The shop owner received 10 real shillings from the tobaccoist, paid 4 to the con man, then paid 10 to the tobaccoist. He also gave up the chocolates, which were worth 6 shillings. 10 – 4 – 10 – 6 = 10 shillings lost.

    Reply
  7. Mom Avatar
    Mom

    I say he is out 14 shillings and the chocolates!

    Reply
  8. Tyler Machovina Avatar
    Tyler Machovina

    Ok, so I haven’t looked at any of the other comments yet. In purely fiat terms he has lost 4 shillings. He exchanged the fake note worth 0 shillings for a 10 shilling note (+10) and gave the customer 4 shillings in change (-4). So the current tally is at (+6). The shopkeeper then must pay back the tobacconist 10 shillings for the false note (-10). This leaves the shopkeeper at -4 shillings. If we account for the chocolate that was effectively stolen (-6) the shopkeeper has lost 10 shillings.

    Reply
  9. Amanda S. Avatar
    Amanda S.

    The storekeeper is down 4 shillings plus the cost of the chocolate. *

    The shopkeeper gains 10 shillings from the fake note that he exchanges for the real one. He then gives 4 of those shillings away in change to the customer, so he is at 6 shillings profit. The shopkeeper then has to give those 6 plus 4 more shillings to the tobaccoist. The shopkeeper has effectively lost 4 shillings, and whatever the cost of the chocolate was.
    * (It is not likely that the shopkeeper originally paid 6 shillings for the chocolate, because this would mean a loss in profit. Whatever he paid for the chocolate in the first place is what he has lost, plus the 4 shillings in change.)

    Reply
  10. cagrimmett Avatar
    cagrimmett

    The answer is 10 shillings. For a good explanations, see Mort, Nonarchist, and Tyler Machovina’s posts.

    Reply

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