SOLUTION: Hi I just need to see if my child is headed in the right direction towards solving this.. Its a long answer where the process seems to be more important than the outcome. POW Co

Question 174899: Hi I just need to see if my child is headed in the right direction towards solving this..
Its a long answer where the process seems to be more important than the outcome.
POW
Consider the case of Loki the Llama, the enterprising ,but eccentric owner of a small mango grove in a remote desert oasis.Loki's harvest, which is worth its weight in gold, consists of 3000 mangos. The marketplace where the harvest can be sold is 1000 miles away.
Loki must walk to the market, but she can carry at most 1000 mangos at a time.Futhermore, being a llama, Loki eats one mango during each and every mile she walks. So Loki can nver wal anywhere without mangos.
How many mangos can the enterprising and smart LOKI transport to the market?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Well, it's clear that Loki the Llama cannot make the 1000-mile journey to the market place in one trip because she would end up mango-less (it would be fruitless!).
Nor could she even go more than half way if she is to return to the source of her mangos.
So, clearly, she must set up caches of mangos on her way to market so that she can get some of the mangos to market.
Here's one approach:
Start with a full load (1000 mangos), go 250 miles (eat 250 mangos in the process), deposit 500 mangos in the first cache and return (eat 250 more mangos) to the source. This will take care of the first 1000 mangos. (1000-250-500-250 = 0)
Second trip, start with a full load (1000 mangos), go 250 miles to the first cache, pick up 250 mangos to replace the 250 eaten (now Loki has a full load again), and go 250 miles more to the second cache. Deposit 500 mangos in the second cache and return to the first cache to pick up the remaining 250 mangos and return to the source. (1000-250+250-250-500-250+250-250 = 0)
Third trip, pick up the remaining 1000 mangos, go 500 miles to the second cache, pick up the 500 mangos there to replace those eaten (now Loki has a full load of 1000 mangos), and proceed the remaining 500 miles to the market place with 500 mangos remaining for sale. (1000-500+500-500 = 500).
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