Interesting thinking-the largest number of Apple remaining

A and B are 1000 metres apart, and 3000 apples are shipped to B. One camel can only

Put 1000 apples on your shoulders, and you must eat an apple each day. If you don't give it, camels will not walk. If you use this

How many apples are there at most from the first place to the second place?

 

Solution: the first type of solution (illustration) is also the most common method, but the remaining Apple

The most, here is just a way of thinking.

(1) from the starting point of location a, dig up 1000 apples, and walk 400 meters toward location B, then put down 200

An apple, and then return to the starting point. At this time, there is no apple on the back of the camels.

(2) carry 1000 more apples at the starting point, walk 400 meters to B, and then put down 200

An apple, and then return to the starting point. At this time, there is no apple on the back of the camels.

(3) carry 1000 more apples at the starting point, and walk 400 meters in the direction of B.

400 apple back, now the camels carry a total of 1000 apple back, and then finish the rest

600 meters, and 400 apples left.

The result obtained by this solution is not the maximum value. From the mathematical point of view, the maximum remaining amount of Apple can be obtained. See figure 2.

Solution.

 

Method 2:

(1) because the total number of apples is 3000, and camels can only carry one or 1000 at a time, it is concluded that

The first round trip is: (3000/1000) * 2-1 = 5 times (this: according to

It consumes apple to count ).

(2) The first round of consumption can only be 1000 yuan, the most appropriate, then each

Forward: 1000/5 = 200 meters. Then put down 600 Apple S and return to the starting point.

(3) Place 1000 apples at the starting point, walk 200 meters, put down 600 apples, and return to the starting point.

(4) Renew the remaining 1000 apples at the starting point again and go to 200 meters.

To the starting point, all the remaining apples have been shipped to 200 meters, total remaining:

3000-200*5 = 2000 apple.

(5) The second round trip is: (2000/1000) * 2-1 = 3 times (this is based on no consumption

Apple to count ).

(6) Similarly, if the number of apples consumed in the second trip is also 1000, then proceed:

1000/3 = 333.33, rounded up to 334.

(7) place 200 apples at 1000, move forward 334, reach 534, put

Next 332 apples, and then return to 200 meters.

(8) then, place the remaining 200 apples at 1000 metres and move forward 334 metres to 534 metres.

At this time, the number of apples is: 1000-334 + 332 = 998.

(9) There are 998-(1000-534) = 532 Apple's remaining routes.

The maximum remaining number of apples obtained by this solution is 532.