A banana plantation is located next to a desert. The plantation owner has 3000 bananas that he wants to transport to the market by camel, across a 1000 kilometre stretch of desert. The owner has only one camel, which carries a maximum of 1000 bananas at any moment in time, and eats one banana every kilometre it travels. What is the largest number of bananas that can be delivered at the market?
2006-10-19 23:24:41 · 4 answers · asked by devesh y 2 in Science & Mathematics ➔ Mathematics
Form the perspective of "moving bananas around", one can devise this simple scheme: load up the camel with 1000 bananas, walk one km (the camel eats one banana), drop 998 bananas there and come back with the other banana as food. You do that again for a second load, and then for a 3rd load, except that, on the 3rd trip, you stay there, dropping 999 bananas. So you have 2995 bananas 1 km from the plantation, with the camel on the spot, ready to go. So, in essence, you can move between 2000 and 3000 bananas at 5 bananas per km.
Therefore, you can move the load 200 km consuming 1000 bananas, and can have 2000 bananas 200 km from the plantation.
Then the rule of transportation change, because you have two loads to carry instead of 3, so you can move a load between 1000 and 2000 bananas at 3 bananas per km.
The next 1002 bananas can therefore take you a further 334 km, where you would have 998 bananas, but you would be 534 km from the plantation, or 466 km from the market. The camel would eat 466 bananas from the 998 you have left, leaving you with 532 bananas by the time the market is reached.
(The actual theoretical solution would be 533.333 bananas, but I doubt that the problem allows fractional bananas. Besides, it is hard to imagine that an unladen camel would eat the same as one loaded with 1000 bananas, but we have to work with the problem as stated, don't we?)
2006-10-20 01:33:01 · answer #1 · answered by Vincent G 7 · 1⤊ 0⤋
Try this:
Let the starting point be location one.
Let the 250K distance across the desert be location 2.
Let the 500K distance across the desert be location 3.
Let the four stop be the market location called location 4.
Load the camel up with 1000 bananas and march the camel 250K across the desert. Unload 500 bananas and return to location point two. At this point the camel has eaten 500 bananas (250 each way).
Load the camel up with another 1000 bananas and march him again to location two. Again unload 500 bananas and return to location one. At this stage the camel has eaten 1000 bananas. Now load up the camel with the remaining 1000 bananas and march him to location two (250K). At this stage there is 1750 bananas left ( 500 + 500 + 750 on the camel).
Now load the camel with a full load (1000) bananas and march him to location three - the 500K mark. Unload 500 bananas and return to location two. At this stage another 500 bananas has been eaten. Load up the camel with the remaining bananas (750) and march him to location three. When the camel get to location three this time, he will be left with 500 bananas on board because he would have eaten 250 bananas on the way. Load up the remaining bananas (500) that is at location three, so the camel has a full load of 1000 bananas and march him the remaining distance to location four (final stop). Since the remaining distance is 500K, the camel will be left will 500 bananas.
Answer - 500 bananas.
However, this does not take into consideration the camel's trip home. It that's an issue, it might be best not to make the trip at all and just keep the bananas for the camel.
2006-10-20 00:18:55 · answer #2 · answered by Brenmore 5 · 0⤊ 0⤋
zero? actually, he would end up with -3000 bananas as every time the camel makes it to the market all the 1000 bananas it can carry are eaten already and either it does not make it back across the desert without bananas or it uses up another non-existent banana on the way back.. lol...
I think the owner should carry some bananas as well so at least some of them make it.. ha ha..
2006-10-19 23:48:47 · answer #3 · answered by sidulrike 4 · 0⤊ 0⤋
I suppose he can stop in the desert. Drop off some bananas and go back home to get some more?
- Pick up 1000 bananas at home.
- At 400 km drop off 200 bananas.
- Keep 400 and go back home.
- Make three trips and we have 200+200+600=1000 bananas at the 400 km point. (No need for the last return trip.)
- Pickup all bananas and go to the market
- Sell the 400 bananas left.
Edited later: Kudos to Brenmore! Two stops in the desert wins.
2006-10-20 00:06:53 · answer #4 · answered by cordefr 7 · 0⤊ 0⤋