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Posers and Puzzles

Posers and Puzzles

  1. 08 May '05 23:21
    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 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?
  2. 09 May '05 02:14
    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?
    it is either nil or 10 not to sure which one yet
  3. 09 May '05 02:19
    well I could get 1250 KG of grass there at this moment, but that amount probably should be bigger.
  4. 09 May '05 18:41
    Originally posted by Coconut
    well I could get 1250 KG of grass there at this moment, but that amount probably should be bigger.
    I agree you should be able to do a bit better than 1250.
  5. 09 May '05 21:03
    call 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!
  6. 09 May '05 21:04
    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
  7. Standard member ark13
    Enola Straight
    09 May '05 22:20
    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
    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.
  8. 09 May '05 22:53
    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
    See ark13's reply.

    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.
  9. Standard member Nemesio
    Ursulakantor
    13 May '05 05:20 / 1 edit
    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?
    The most I was able to get there was 750kg, but I don't have any magical formulae, just
    a process that seemed reasonably intuitive to me.

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

    Nemesio
  10. Subscriber AThousandYoung
    It's about respect
    13 May '05 10:52
    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 the camel half the distance in one go, I lose all my grass to the camel (loss of 100% per iteration, 1 iteration).

    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.
  11. Standard member Nemesio
    Ursulakantor
    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
  12. 14 May '05 06:56
    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
    19 x 1000 = 19 000, not 1900
  13. Standard member Nemesio
    Ursulakantor
    14 May '05 17:04
    Originally posted by Mephisto2
    19 x 1000 = 19 000, not 1900
    Stop clouding the issue with the facts

    Nemesio
  14. Subscriber AThousandYoung
    It's about respect
    14 May '05 18:04 / 3 edits
    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
    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.

    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.
  15. Standard member Nemesio
    Ursulakantor
    14 May '05 23:14 / 1 edit
    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 suppl ...[text shortened]... across the desert (thus having 8100kg in Damascus).

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

    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