Is this question difficult, or easy?

Try,

To answer your initial question, this is a great mathematical question. I don't think it will interest those who don't have a strong math nerd streak.

But, I loved it! Thanks.

I'm having trouble following you ebrown... I can't get past 444 bananas.

Ok Step by Step.

1. Load 1000 bananas I bring them to the 200 mile marker
Bananas at start = 2000
Bananas at 200 iles = 800
Bananas eaten = 200

2. Go back and get 1000 more bananas (eating 400 on the rt)
Bananas at start = 1000
Bananas at 200 miles = 1400
Bananas eaten = 600

3. Go back and get 1000 more bananas (eathing another 400)
Bananas at start = 0
Bananas at 200 iles = 2000
Bananas eaten = 1000

4. Go an addition 333.33 miles with 1000 bananas (eating 333.33 on the way
Bananas at 200 miles = 1000
Bananas at 533.33 miles = 666.66
Bananas eaten = 1333.33

5. Go back to 200 mile mark and get 1000 bans (eating 666.66 on the rt).
Bananas at 200 miles = 0
Bananas at 533.33 miles = 1000
Bananas eaten = 2000

6. Grab the 1000 bananas and go to the market (now 467.66 miles away).
Bananas at 533.33 miles = 0
Bananas at market = 533.33
Bananas eaten 2467.66

After all this work I am going to sell the 533 bananas. I am going to eat the remaining 1/3 banana with the camel.

Doesn't work.

If you go 200 miles -- you can only leave 600 bananas. (You need 200 to get back to start.)

Okay, now I got you... Thanks

Frank 600 + 600 + 800 leaves 2000 at the 200 mile marker.

Frank, It works.

I account for the 200 bananas to go back to start in steps 2 and 3. To get 2000 to the 200 mile mark I need to go forward 3 times. I only need to go back twice.

It works. And I am 99% sure there is no better way to do it.

Hummm...you may have sold me on this.

I'll look it over again, but your reasoning sounds good at the moment.

May I thank you all for your contributions, and in particular ebrown_p who supplied the answer to the puzzle and the question. It is more suited to a formula than pure logic.

The full answer I have is as follows:

It initially seems that the answer is 0 since it would take 3 trips to the market and the camel will have eaten all 3000 bananas by then. Actually, if the camel tried to take 1000 bananas 1000 miles it couldn't get back unless it picked up another 1000 bananas at the market. But this doesn't take into account that his load is going to be reduced along the way as the camel eats the bananas.

Let's take it mile by mile. Since initially there are 3000 bananas and the camel only can carry 1000 at a time, the camel must make 3 trips forward: forward with the 1st 1000, back, forward with the 2nd 1000, back, and forward with the last 1000. Note that it takes 3 trips forward and 2 trips back to go the mile. For the 1st mile the camel carries 1000 bananas forward and eats 1, it eats 1 banana on the way back, carries 1000 bananas forward and eats 1, eats 1 going back, and 1000 bananas forward and eats 1. So, after the 1st mile there are 1000 - 1 - 1 + 1000 - 1 - 1 + 1000 - 1 or 2995 bananas left. So initially, for every mile travelled forward (in 3 trips), the camel eats 5 bananas.

However, after 200 miles the load will be down to 2000 bananas and the camel only needs to make 2 trips forward: forward, back, forward. For each of the next 333 and 1/3 miles the camel will eat 3 bananas to carry the load ahead. Therefore, after 533 1/3 (200 + 333 1/3) miles the load will be eaten down to 1000 bananas.

For the next 466 2/3 miles till the camel gets the market, it will eat 1 banana per mile to carry the load. 1000 - 466 2/3 = 533 1/3 bananas left. So the camel will eat a total of 200 * 5 + 333 1/3 * 3 + 466 2/3 = 2466 2/3 bananas to get the entire 3000 bananas to market so the grower will have 533 1/3 bananas left to sell. Maybe 533 because who would want to eat a banana 2/3 of which a smelly camel has eaten.
Also, he'll have to sell his camel there because he doesn't have the bananas to get it back.

Before returning to the realm of puzzles, may I leave you with an old favourite?
Not original, but seemingly impossible from the information supplied. However, I assure you the answer is there and no trickery involved. Again, many thanks.

At a party, you overhear another guest asking the age of the hosts' three children.
The host gives the following information to the guest:
• Assume each kid's age is a whole number.
• The product of their ages is 72
• The sum of their ages is the same as the guest's house number
The guest obviously knows her own house number but, after thinking for a bit,
she is forced to ask the host for additional information. The host then says:
• Well, my oldest child likes strawberry ice cream.

You now have all the information you need to determine the ages. How old is his oldest child

Assuming the host does not have twins -- the oldest child is 9.

If the host happens to have twins -- (two younger children) the oldest child may be either 8 or 9.

Before reaching an answer, you would have to have worked out the house number. What is that number

Without that number, it can only be a guess.

This question has been answered in another place; therefore, I give the full answer below for anyone that is still puzzled.

The full answer is as follows:
This is much like Student Ages question although a bit easier. You first must factor 72 which breaks down into 1x2x2x2x3x3. Combining these numbers to make 3 ages reveals 11 combinations: (1 2 36), (1 3 24), (1 4 18), (1 6 12), (1 8 9), (2 2 18), (2 3 12), (2 4 9), (2 6 6), (3 3 8), and (3 4 6).

The host says that their sum is equal to the house number of the guest. If the guest has to ask for more information then some of the combinations must add up to the same number. By adding up all of the combinations, we find that (2 6 6) and (3 3 8) both add up to 14 so the house number must be 14 and one of the combinations must be correct.

Then the host says that the oldest likes strawberry ice-cream which tells you that there is an oldest. Since (2 6 6) implies that two of his children have the same age, the answer must be (3 3 8).

So his oldest child is 8. :wink:

I believe since the guest was in doubt, there were two combinations possible for the same house number. The two combinations are 2,6,6 and 3,3,8.
Since the oldest son likes ice cream, it's pretty obviously 3,3,8.

UUps! Only reas 1st page - I thought Frank's was the last post

Well' at least a nice excel workout for me

3000 Bananas
I was able to reach the market with 600 bananas to sell. The solution needs to be viewed in Excel, though, as it isn't much of a formula but more of an application of a logical algorithm of how to maximize the camel's movements and I outlined the actual steps in Excel. I've attached it in text format here, but it won't make much sense as the spacing isn't right. Does it work?
Start Mile 1 Mile 2 Mile 3 Mile 4 Mile 5 Mile 6 Mile 7 Mile 8 Mile 9 Mile 10 Bananas Remaining
30 30
19 10 29
19 9 28
8 19 27
8 8 10 26
8 8 9 25
8 7 9 24
0 14 9 23
0 3 19 22
0 3 8 10 21
0 3 8 9 20
0 3 7 9 19
0 0 9 9 18
0 0 0 17 17
0 0 0 6 10 16
0 0 0 6 9 15
0 0 0 0 14 14
0 0 0 0 3 10 13
0 0 0 0 3 9 12
0 0 0 0 0 11 11
0 0 0 0 0 0 10 10
0 0 0 0 0 0 0 9 9
0 0 0 0 0 0 0 0 8 8
0 0 0 0 0 0 0 0 0 7 7
0 0 0 0 0 0 0 0 0 0 6 6

Multiply by 100 to see everything in terms of the 3000 bananas and the 1000 miles

Welcome to the forum Howarddygo, apologies for missing your reply. I am intrigued as to how you decided to make a year old problem your first post. You make a most interesting point. However, I am a little unsure if your reply proves a better answer. Can you explain in a clearer way? If you are correct, you will have raised the bar and set a new standard. Look forward to reading more of your posts.

Hi, Tryagain. I sort of found this site by accident when I was looking for an interesting problem to keep me busy during one of my dull days. I found some bugs in my answer and will make some adjustments and get back to you on it.

It is good to have you with us. I am sure you will find enough to keep you occupied for a very long time. Be sure to check out the rest of the site.

Thanks!
I double checked my answer. It was wrong. It works on a micro scale but it only hit 500 once it became 3000 bananas and 100 bananas gets wasted somewhere in the 400th mile.
It was fun playing around with it though.
I look forward to enjoying the rest of this site.

TTH:

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