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Posers and Puzzles

Posers and Puzzles

  1. Standard member talzamir
    Art, not a Toil
    12 May '12 08:53
    Five guys have had a party in the desert, and take a taxi to get home. They agree that each of the four pays a share of the cab fare that reflects the costs that are caused by taking him home, as is, after all, fair. Calling the cab in the first place costs $8, and there is an extra $1 per mile.

    From the party place at (0,0) the taxi drives
    * drop Andrew off at (3,4)
    * drop Bob off at (6,0)
    * drop Chuck off at (9,0)
    * drop Dan off at (9,4)

    Ed doesn't need to get into the taxi at all, as this time the party was at Ed's home.

    The total cost is $8 + $5 + $5 + $3 + $4 = $25.

    How much should everyone pay for the cab fair?
  2. 13 May '12 14:46
    You've posted this one a while ago, with islands and a ship instead of a desert and a cab.
  3. Standard member talzamir
    Art, not a Toil
    19 May '12 19:15
    oops! ^^ Sorry about that. A nice problem anyhow. I thought of it again when thinking of the Roman inheritance, as they both look simple enough on top but it is hard to justify one answer to be the only correct one.
  4. Subscriber Pianoman1
    Nil desperandum
    20 May '12 06:49
    Originally posted by talzamir
    Five guys have had a party in the desert, and take a taxi to get home. They agree that each of the four pays a share of the cab fare that reflects the costs that are caused by taking him home, as is, after all, fair. Calling the cab in the first place costs $8, and there is an extra $1 per mile.

    From the party place at (0,0) the taxi drives
    * drop Andre ...[text shortened]... total cost is $8 + $5 + $5 + $3 + $4 = $25.

    How much should everyone pay for the cab fair?
    This is similar to the restaurant conundrum:

    Three customers go to a restaurant and have a meal. The bill comes to £25. They each a give a £10 note to the waiter. He can't work out how much change to give back to each customer, so he keeps £2 tip and gives £1 back to each customer.
    So the customers have paid £9 each, (£27), the waiter has £2. Where is the missing £1?
  5. 20 May '12 13:13 / 1 edit
    Originally posted by talzamir
    oops! ^^ Sorry about that. A nice problem anyhow. I thought of it again when thinking of the Roman inheritance, as they both look simple enough on top but it is hard to justify one answer to be the only correct one.
    That's true. I would give A, B, C, and D a weight equal to the total costs minus the costs they would've had without that person. So for A it would be $25 - ($8 + $6 + $3 + $4) = $25 - $21 = 4
  6. Standard member forkedknight
    Defend the Universe
    21 May '12 21:30
    Originally posted by Pianoman1
    This is similar to the restaurant conundrum:

    Three customers go to a restaurant and have a meal. The bill comes to £25. They each a give a £10 note to the waiter. He can't work out how much change to give back to each customer, so he keeps £2 tip and gives £1 back to each customer.
    So the customers have paid £9 each, (£27), the waiter has £2. Where is the missing £1?
    Surprisingly hard to see how people think about this the wrong way.

    The customers each paid $9 x 3 = $27: true
    The waiter has $2: true
    The waiter's $2 is separate from the $27 the customers paid: false

    $27 (paid by the customers) - $2 (kept by the waiter) = $25 (the bill)
  7. Standard member wolfgang59
    Infidel
    22 May '12 09:31
    Originally posted by forkedknight
    Surprisingly hard to see how people think about this the wrong way.

    The customers each paid $9 x 3 = $27: true
    The waiter has $2: true
    The waiter's $2 is separate from the $27 the customers paid: false

    $27 (paid by the customers) - $2 (kept by the waiter) = $25 (the bill)
    But what happened to the $30 they paid?
  8. Standard member forkedknight
    Defend the Universe
    22 May '12 18:41
    Originally posted by wolfgang59
    But what happened to the $30 they paid?
    Serious question? The other $3 was returned in change.

    $30 - $3 (change) - $2 (waiter) = $25 (bill)
  9. 26 May '12 23:21
    Originally posted by Pianoman1
    This is similar to the restaurant conundrum:

    Three customers go to a restaurant and have a meal. The bill comes to £25. They each a give a £10 note to the waiter. He can't work out how much change to give back to each customer, so he keeps £2 tip and gives £1 back to each customer.
    So the customers have paid £9 each, (£27), the waiter has £2. Where is the missing £1?
    The last bit:
    So the customers have paid £9 each, (£27), the waiter has £2. Where is the missing £1?
    9*3 + 2 =....
    i.e. it is wrongly adding what the customers have paid in total to what they paid the waiter

    Should read:
    So the customers have paid £9 each, (£27), the waiter has £2 and the restaurant has its £25
    9*3 - 2 = 25

    or
    So the customers paid £10 each, (£30), the waiter has £2, the customers got back £3 and the restaurant has its £25
    10 - 2 - 3 = 25