- 08 May '05 23:21The distance between Cairo and Damascus is 1000 miles. You have 10,000 kilograms of grass you want to move from Cairo to Damascus using your camel. However, two difficulties arise:

1. Your camel will not budge unless you continuously allow him to eat grass, and he consumes 1 kilogram of grass per mile.

2. The maximum carrying capacity of the camel is 1000 kilograms.

Will you be able to get any of the grass to Damascus? If so, what is the maximum amount you will be able to transfer? - 09 May '05 02:14

it is either nil or 10 not to sure which one yet*Originally posted by davegage***The distance between Cairo and Damascus is 1000 miles. You have 10,000 kilograms of grass you want to move from Cairo to Damascus using your camel. However, two difficulties arise:**

1. Your camel will not budge unless you continuously allow him to eat grass, and he consumes 1 kilogram of grass per mile.

2. The maximum carrying capacity of the camel is ...[text shortened]... t any of the grass to Damascus? If so, what is the maximum amount you will be able to transfer? - 09 May '05 21:03call this incredibly stupid (don't take it literally) but i don't believe you can get any grass over at all:

1000-mile distance

1000-kg at a time

Camel will eat 1kg per mile, so it will eat ALL of the grass, leaving you on the camel at the end of the path, with no grass, where as there is tons of grass back where you came from, which you can't get to because you have no more grass to feed the camel. PLUS, you can't carry 1000 kg of grass for the camel to eat, because YOU WEIGH SOMETHING (and i doubt you'ld walk 1000 miles), so your camel will refuse to budge. Phew! - 09 May '05 22:20

The thing you're missing (I think) is that the camel could put the grass it's carrying down at some point during the journey and return.*Originally posted by Duck Duck Goose***1000 miles**

1000 kg maximum carrying load

1 kg of grass per mile... so

camel eats all of the grass now you're stuck in Damascus - 09 May '05 22:53

See ark13's reply.*Originally posted by Duck Duck Goose***1000 miles**

1000 kg maximum carrying load

1 kg of grass per mile... so

camel eats all of the grass now you're stuck in Damascus

You should be able to convince yourself that it is possible to transfer at least a portion of the grass.

For example: Starting in Cairo, load up 1000 kg of grass. Take it 400 miles and drop off 200 kg of grass and return to Cairo with the remaining 400 kg. Load up 1000 kg again and return to the 400 mile marker. Now you have 800 kg there (600 on you plus the 200 you already dropped off there) and only 600 miles to Damascus. So, you can get 200 kg to Damascus just using this (far from optimal) method. This should at least convince you that some grass transfer is possible.

The question is if you optimize your strategy, how much can you get there? The optimal strategy should utilize all of the grass and should minimize the number of miles tracked by the camel. - 13 May '05 05:20 / 1 edit

The most I was able to get there was 750kg, but I don't have any magical formulae, just*Originally posted by davegage***The distance between Cairo and Damascus is 1000 miles. You have 10,000 kilograms of grass you want to move from Cairo to Damascus using your camel. However, two difficulties arise:**

1. Your camel will not budge unless you continuously ...[text shortened]... ? If so, what is the maximum amount you will be able to transfer?

a process that seemed reasonably intuitive to me.

I can't get 1250kg like coconut, though...

Nemesio - 13 May '05 10:52

If I take the camel half the distance in one go, I lose all my grass to the camel (loss of 100% per iteration, 1 iteration).*Originally posted by davegage***The distance between Cairo and Damascus is 1000 miles. You have 10,000 kilograms of grass you want to move from Cairo to Damascus using your camel. However, two difficulties arise:**

1. Your camel will not budge unless you continuously allow him to eat grass, and he consumes 1 kilogram of grass per mile.

2. The maximum carrying capacity of the camel is ...[text shortened]... t any of the grass to Damascus? If so, what is the maximum amount you will be able to transfer?

If I take it one quarter of the distance, and then another quarter once it's all been taken to 250 miles, I lose half my grass, and then half of that, so I am left with one quarter of my supply at 500 miles, and one eighth at 750 miles, or 1250 at 750 miles, and 625 at 1000 miles (loss of 50% per iteration, 4 iterations).

If I take it one tenth of the distance at a time, I lose 20% per iteration, and there are ten iterations; 8000, 6400, 5120, 4096, 3276, 2620, 2096, 1670, 1336 at 900 miles; and then 1236 at 1000 miles.

It looks as though the smaller the distance at one go, the more you can get there. There must be some kind of limiting problem; the limit as distance per iteration approaches zero of the amount that reaches the end after all the iterations.

*Busts out the calculator program*

Let's say the distance per iteration were one fiftieth of the total distance, or 20 miles per. The loss would be 40/1000 or 4% per iteration for fifty iterations (multiply by 96% 50 times).

Ten iterations 6648; 20 iterations; 4420; 30, 2939...it looks like we're losing a third per 10 iterations approximately. 40, 1953; 50, 1298. The smaller each iteration is, the more gets there in the end, looks like. I wonder what the limit is, and how would I find it? It would be some sort of calculus problem. - 14 May '05 05:26 / 1 edit
*Originally posted by AThousandYoung***If I take it one quarter of the distance, and then another quarter once it's all been taken to 250 miles, I lose half my grass, and then half of that, so I am left with one quarter of my supply at 500 miles, and one eighth at 750 miles, or 1250 at 750 miles, and 625 at 1000 miles (loss of 50% per iteration, 4 iterations).**

This is not quite right. If you take your entire amount of grass to 250 miles, you will have

5250kg because you will not be making the return trip to pick up nothing. I don't know if this

affects things for your calculations, though.

And, if you try to do what you are suggesting for the 10th distance, you'll find that it doesn't quite

work out like you say. The first iteration has 8100, the second a maximum of 6400, the third

a maximum of 5100, the fourth a maximum of 4000, fifth - 3200, sixth - 2500, seventh - 2000,

eighth - 1600, ninth - 1400, tenth - 1100. (I think.)

So, the best way to do it is to take everything in one-mile increments. To take the 10,000 kg

one mile will cost 19 kg in food. Multiply this by 1000 (i.e., 1900 kg) and you have the total

expense for taking it across the desert (thus having 8100kg in Damascus).

Nemesio - 14 May '05 06:56

19 x 1000 = 19 000, not 1900*Originally posted by Nemesio**Originally posted by AThousandYoung*

[b]If I take it one quarter of the distance, and then another quarter once it's all been taken to 250 miles, I lose half my grass, and then half of that, so I am left with one quarter of my supply at 500 miles, and one eighth at 750 miles, or 1250 at 750 miles, and 625 at 1000 miles (loss of 50% per iteration, 4 i ...[text shortened]... the total

expense for taking it across the desert (thus having 8100kg in Damascus).

Nemesio - 14 May '05 18:04 / 3 edits

Yes, you're right. However when taken to the limit of infinitely small distances and infinitely large iterations, this little addition goes to zero. I think.*Originally posted by Nemesio**Originally posted by AThousandYoung*

If I take it one quarter of the distance, and then another quarter once it's all been taken to 250 miles, I lose half my grass, and then half of that, so I am left with one quarter of my supply a ...[text shortened]... it across the desert (thus having 8100kg in Damascus).

Nemesio

No wait...I see your point. I was only taking into account the last iteration not having to go back. Hmm. I need to think about this. - 14 May '05 23:14 / 1 edit

If I take it in a total of 25 forty-mile increments, my amounts are:*Originally posted by Nemesio*[/b]*Originally posted by AThousandYoung*

[b]If I take it one quarter of the distance, and then another quarter once it's all been taken to 250 miles, I lose half my grass, and then half of that, so I am left with one quarter of my suppl ...[text shortened]... across the desert (thus having 8100kg in Damascus).

Nemesio

40 - 9240 kg (920 kg each time, plus 40 kg on the final trip).

80 - 8480 kg

120 - 7800 kg

160 - 7200 kg

200 - 6600 kg

240 - 6080 kg

280 - 5560 kg

320 - 5120 kg

360 - 4680 kg

400 - 4320 kg

440 - 3960 kg

480 - 3680 kg

520 - 3400 kg

560 - 3120 kg

600 - 2840 kg

640 - 2640 kg

680 - 2440 kg

720 - 2240 kg

760 - 2040 kg

800 - 1840 kg

840 - 1720 kg

880 - 1600 kg

920 - 1480 kg

960 - 1360 kg

1000 - 1240 kg

That isn't so hot.

With 20 fifty-mile iterations, you get:

50 - 9050 kg (depositing 900 kg each time plus an extra 50 on the final trip)

100 - 8100 kg

150 - 7250 kg

200 - 6500 kg (100 kg worse than forty-mile increments)

250 - 5850 kg

300 - 5300 kg

350 - 4750 kg

400 - 4300 kg (20 kg worse than forty-mile increments)

450 - 3850 kg

500 - 3500 kg

550 - 3150 kg

600 - 2800 kg (40 kg worse than forty-mile increments)

650 - 2550 kg

700 - 2300 kg

750 - 2050 kg

800 - 1800 kg (40 kg worse than forty-mile increments)

850 - 1650 kg

900 - 1500 kg

950 - 1350 kg

1000 - 1200 kg (40 kg worse).

If I do it in 40 twenty-mile increments:

20 - 9620 kg

40 - 9240 kg

60 - 8860 kg

80 - 8520 kg

100 - 8180 kg

120 - 7840 kg

140 - 7540 kg

160 - 7240 kg

180 - 6940 kg

200 - 6680 kg (better than either of the above test cases)

220 - 6420 kg

240 - 6160 kg

260 - 5900 kg

280 - 5680 kg

300 - 5460 kg

320 - 5240 kg

340 - 5020 kg

360 - 4800 kg

380 - 4620 kg

400 - 4440 kg (considerably better than either above case)

420 - 4260 kg

440 - 4080 kg

460 - 3900 kg

480 - 3760 kg

500 - 3620 kg

520 - 3480 kg

540 - 3340 kg

560 - 3200 kg

580 - 3060 kg

600 - 2920 kg (still better)

620 - 2820 kg

640 - 2720 kg

660 - 2620 kg

680 - 2520 kg

700 - 2420 kg

720 - 2320 kg

740 - 2220 kg

760 - 2120 kg

780 - 2020 kg

800 - 1920 kg (still better)

820 - 1860 kg

840 - 1800 kg

860 - 1740 kg

880 - 1680 kg

900 - 1620 kg

920 - 1560 kg

940 - 1500 kg

960 - 1440 kg

980 - 1380 kg

1000 - 1320 kg (!!!!)

I don't have the patience to do 100 ten-mile increments, but intuition tells me that this will be

better yet. Similarly, one-mile increments, I would expect would be best (despite the problems

with my summary above).

Davegage, am I on the right track?

Nemesio