# Rechargeable batteries

We have a rechargeable battery charger, in which there are three connectors to charge three batteries simultaneously. The charge indicator of each of the batteries has four levels: fully discharged, one third charge, two thirds charge and fully charged.

Normally, we put three batteries in it and wait for them to be charged, which takes one hour (every twenty minutes exactly one of the charge levels is completed). However, today we are in a hurry to charge the four batteries of our mp3 that are fully discharged since we only have an hour and a half to charge them.

We could first charge three batteries completely and then charge a single battery leaving the other two spaces, but we don't have two hours for two periods of full charge. We know that if we have a partially charged battery and place it in the charger, the charging cycle continues from the battery charge level.

Can you find a method to charge all four batteries in less than an hour and a half?

Extracted from the problemate.blogspot.com.es page

#### Solution

The solution to this problem is basically to think of thirds of the battery, rather than full batteries. Actually, the charger fills, so to speak, three thirds of the battery in 20 minutes. That is, if we could take full advantage of it, it would charge a battery every 20 minutes, but since three thirds cannot belong to the same battery, it must be replaced.

As we have to charge 4 batteries, the best result we can obtain is to charge them in 80 minutes, since in total 12 thirds have to be filled.

What must be monitored is that the batteries that we place in the charger every 20 minutes always have thirds empty and that all the positions of the charger are full.

If we identify the batteries with the letters A, B, C and D, we can charge ABC in the first 20 minutes, ABD in the second 20 minutes, ACD in the third stretch of 20 minutes (with which A will already be charged) and in the last BCD interval.