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Redglyph

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I have a fun little problem our math teacher asked us at school, to illustrate a point.

Don't hesitate to use ISPOILER / SPOILER tags for the replies. :)

A vacuum cleaner salesman rings at a door and a woman opens. He delivers his speech and the woman says:
- I'll buy your product if you can answer this simple question. I have three kids, the sum of their ages is the number of this house, and the product of their ages is 36. How old are they?
The salesman thinks for a while, then replies:
- I'm sorry but I cannot answer your question...
The woman ponders on this for a few seconds then adds:
- OK, I can tell you the oldest plays piano.
The salesman thinks again, answers and sells his vacuum cleaner.

What are the kids' ages?
 
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HiddenX

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36 = 3*3*2*2*1

All possible solutions:
36= 36*1*1 sum: 38
36= 18*2*1 sum: 21
36= 12*3*1 sum: 16
36= 9*4*1 sum: 14
36= 9*2*2 sum: 13
36= 6*6*1 sum: 13
36= 6*3*2 sum: 11
36= 4*3*3 sum: 10

The salesman can't decide yet, so the number of the house is 13 (He knows the number - he's standing before the house!).
The oldest plays piano => there's only one oldest son (theoretically you can give birth to two kids in one year that are NOT twins, but this is very rare)

=> the correct solution is {9 ,2, 2}
 
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Redglyph

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Well done @HiddenX :)

I was surprised back then that so few found the solution - it was after all a class of advanced mathematics to prepare for the much feared admission exam at uni.

Most people focused on the required age to play the piano or asked the house number. The teacher's point was we had to carefully listen to the whole problem before jumping to any conclusion.

The bit of information that one should not miss here is indeed the fact the problem cannot be solved without additional information. I found it was quite neat. :D
 
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Redglyph

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You need to transport 3000 bananas across 1000 km in the desert. You only have one camel, which can carry a maximum load of 1000 bananas at the same time. The camel must eat 1 banana every km.

How many bananas can you transport at most?

(you can't carry any banana, and you don't need to eat them)
 
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HiddenX

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Does the camel eat bananas if it goes back from an intermediate point as well?
 
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36 = 3*3*2*2*1

All possible solutions:
36= 36*1*1 sum: 38
36= 18*2*1 sum: 21
36= 12*3*1 sum: 16
36= 9*4*1 sum: 14
36= 9*2*2 sum: 13
36= 6*6*1 sum: 13
36= 6*3*2 sum: 11
36= 4*3*3 sum: 10

The salesman can't decide yet, so the number of the house is 13 (He knows the number - he's standing before the house!).
The oldest plays piano => there's only one oldest son (theoretically you can give birth to two kids in one year that are NOT twins, but this is very rare)

=> the correct solution is {9 ,2, 2}
I think the possibility (however rare) of two children born the same year is a bit of a problem for a logic/maths problem. Strictly speaking, that might lead me to reject that as a clear solution, though the most probable.
 
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HiddenX

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Camel Problem
You can't travel in one go, because then the camel eats all bananas.
One solution (if the camel eats bananas for every km)
use intermediate points:

L0 -> L250 -> L500 -> L1000
  1. Load 1000 bananas at L0, travel 250 km, drop 500 bananas at location L250, use the remaining 250 to go back to L0.
  2. Load 1000 bananas again at L0, then travel 250 km to L250, load 250 bananas, so that the camel has 1000 bananas on his back, 250 bananas remain at L250.
  3. Travel 250 km to L500 and drop 500 bananas there, travel 250 km back to L250, load 250 from the last trip and go back to L0.
  4. Load 1000 bananas again, travel 500 km to L500 and load 500 bananas, so that the camel has 1000 bananas on his back.
  5. Go to the destination L1000 with 500 bananas remaining.
This solution is just trial and error - maybe there is a better one.

I couldn't find a mathematical expression to calculate an optimal solution.
 
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Redglyph

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This solution is just trial and error - maybe there is a better one.

I couldn't find a mathematical expession to calculate an optimal solution.
You're quite close but it's possible to optimize. I've taken more or less the same approach but I did a mistake in my calculations the first time, so I did it again by looking for that expression.

The idea is to take steps that leave a multiple of 1000 bananas, because they dictate how many trips are necessary, and thus the cost for each step. So the expression is the cost in banana/km for each of those steps.

1) We could consume the 1000 first bananas, by a lucky guess:
- take 1000 to L200, there's 800 remaining. Drop 600 and get back to L0 (400 eaten)
- take 1000 to L200, drop 600 and get back to L0 (400 eaten)
- take 1000 to L200, drop 800 (200 eaten) => 2000 left.

That's a cost of 1000 for 200 km, so 5 banana per km. That's normal since 3000 bananas require 3 transports, 2 back & forth and 1 final, so 2*2+1 bananas per km.

2) Let's use that approach for the 2nd step. Now there's only 2000 bananas, so 2 transports required, 1 back & forth and 1 final, we expect 2+1 = 3 bananas per km.

To consume 1000 bananas, it would take 333 + 1/3 km. Let's do that and we arrive at L200+333+1/3 = L533+1/3, with only 1000 bananas left.

Or said otherwise,
- take 1000 to L200+333+1/3, drop 333+1/3 (hoping the 1/3 doesn't rot), get back to L200 (666+2/3 eaten)
- take 1000 to L200+333+1/3, drop 666+2/3 (333+1/3 eaten).

3) Final trip, we have 1000 - (533+1/3) km to travel, and the camel eats as many bananas. This leaves us with:

1000 - (1000 - (533+1/3)) = 533+1/3 bananas. Not efficient but after all it's in the desert.

My first reaction was that there would be no banana left, since it would eat all of them, it's quite counter-intuitive. :)

EDIT: fixed a few mistakes
 
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pibbuR

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I wondered where Dart had gone.
 
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pibbuR

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According to my sources (email from Disney+), a new chapter of the Kardashians story is available (in Norway).

pibbuR who is afraid that if he wants to start watching now, a lot of catching up will be needed if he wants to be up to date on the wisdom and lore of the clan.
 
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pibbuR

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Ouch in deed. Are you still there, or have you been evacuated.

pibbuR who likes bad weather, but probably not that bad weather.
 
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JDR13

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Nope, I'm here. I've already lost power. Only have my phone now.

I'm not very close to the beach or in a flood zone, so I should be ok. Might be without power for a few days though.
 
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Ripper

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Yeah, keep safe, and I hope the power doesn't stay out too long. That would get very tedious. It's looking pretty harsh.
 
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