I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!
Monday, January 15, 2007
A traveling man
An explorer wishes to cross a barren desert that requires 6 days to cross, but one man can only carry enough food for 4 days. What is the fewest number of other men required to help carry enough food for him to cross?
Three men, each with 4-days of food head out (day 1). The next day eachhas three days worth of food.
The first man gives one-days rations to each of the other 2. That leaves him with one day's rations to go back.
The other two, now with 4-days of rations continue (day 2)
The next day the second man gives one-days worth of rations to the third man. The second man has 2-days of rations to go back. The third man now has 4-days of rations to make the 4-day trip across the desert.
I always have trouble with this type of problem. But I believe Mr Don has spelled it out.
Although I can't prove it, the minimum required is three men. The first helper only goes one day into the desert. He feeds the other two men during the first day, so that at the beginning of the second day, he only has one day rations left. So he goes back to camp. On the second day, the second helper feeds himself and the explorer. On the beginning of the third day the helper now has two days rations left so he heads back. The explorer is two days into the journey and still has all four days of his food left, so he continues on alone.
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Three men, each with 4-days of food head out (day 1).
ReplyDeleteThe next day eachhas three days worth of food.
The first man gives one-days rations to each of the other 2. That leaves him with one day's rations to go back.
The other two, now with 4-days of rations continue (day 2)
The next day the second man gives one-days worth of rations to the third man. The second man has 2-days of rations to go back. The third man now has 4-days of rations to make the 4-day trip across the desert.
I always have trouble with this type of problem. But I believe Mr Don has spelled it out.
ReplyDeleteAlthough I can't prove it, the minimum required is three men. The first helper only goes one day into the desert. He feeds the other two men during the first day, so that at the beginning of the second day, he only has one day rations left. So he goes back to camp. On the second day, the second helper feeds himself and the explorer. On the beginning of the third day the helper now has two days rations left so he heads back. The explorer is two days into the journey and still has all four days of his food left, so he continues on alone.
The man takes the next flight out of the airport across the desert?
ReplyDelete