# Desert Taxi

talzamir
Posers and Puzzles 12 May '12 08:53
1. 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. ðŸ™‚
3. 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. 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 13:131 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. 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. wolfgang59
Mr. Wolf
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. 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