The postman needs to send the mail to 200 kilometers, but the postman can only carry 120 kilometers of dry food. How much dry food does the postmaster need to reserve in advance?

Mail delivery problem with dry food:

It is known that the postman needs to deliver the mail to 200 kilometers, but the postman can only carry 120 kilometers of dry food. How much dry food does the postmaster need to reserve in advance?

Since the postmaster can only carry 120 of dry food, it is necessary to reserve dry food. So there must be supplies in the middle, but where can we find them? In the middle of the supply, we need to bring it out from the starting point. Another problem is, from the starting point, where can we bring 120 back to get the supply? Select the midpoint as the return point, and then take the 120 replenishment. That is to say: 120 of the dry food, advance 40, then put down 40 of the dry food, and then return to the starting point of the 40 km with 40 of dry food.

In this case, if we want to use 120 of the supply, we need to add 40 dry food at 2 or 3 nodes. Okay. Now, if you want to have 40 dry food at Node 3. Then we need to start from 2 with 120 of dry food to ensure that there is 40 of dry food in 3 places. Then 120 of the dry food at 2 sites is divided into 3*40 for delivery, that is, 1-> 2 three times, that is, 120*3 is required to ensure that 40 of the dry food at 3 nodes. Then, only 1*120 of dry food is required for two places to ensure that 40 of dry food is available for two places. Therefore, 120*1 + 120*3 = 480 dry food is required. With the guarantee of dry food in the middle, we should start from 1 with 120 of dry food. In this way, we need 480 + 120 of dry food in total. Take 120 to 2 and spend 40 and then supply 40. In this way, the entire process can be completed. The following is an image

The postman needs to send the mail to 200 kilometers, but the postman can only carry 120 kilometers of dry food. How much dry food does the postmaster need to reserve in advance?