Hey friend,

In this episode, I show how to solve problems backwards on a simple problem of having to bring precisely 6L of water from the river when you only have 4L and 9L water bins.

If you prefer watching, you can find the YouTube video here. If reading is your thing, then enjoy the transcript below.

Welcome to The Daily Recall show. I'm your host, Vasili.

Today you will learn why and how to solve problems backwards.

I'll start from an example. Imagine that you have to bring from the river 6L of water. But you’ve got only two water bins, a 4L one and a 9L one. How do you do that?

When I first heard of this problem, I jumped to brainstorming. "Yeah we can have four here and then fill out the big one and then refill.." I was trying out different methods of solving the problem without thinking about how approach it at all.

But the right way to approach this problem is to work backwards from the ideal solution.

What do I mean by ideal solution?

If we have two water bins, one of 9L and one of 4L, then the only way we can get back with 6L liters of water is by having 6L liters in the big one. That’s the end result. That’s the solution we're aiming for; to somehow have 6L of water in that big 9L water bin.

And that’s precisely where we need to start from. And then we just need to work backwards from that end result. And if you do that, then it turns into a very simple problem. You can pause reading for a second and try solving for yourself and I will explain how to actually do that in the next paragraph.

The way we get 6L in a 9L water bin is by having exactly 3L taken out of it. How do we do that? How do we take 3L out of a 9L water bin if we only got the 4L water bin?

The way we do is by turning the 4L bin into a 3L liter bin. How do we do that? By having 1L filled in there already, right? That’s how we would turn the smaller one from being a 4L into a 3L water bin.

The last question is, how do we get exactly one liter filled in a 4L bin. And that’s actually a fairly simple problem because we can get 1L by fully filling in the 9L water bin and then taking it and filling the 4L bin out of it two times. 9-4-4=1. That’s how we get 1L left in a 9L bin, and then we move it to the smaller one, refill the 9L full again and take out exactly 3L by filling the small one to the edges.

By following this backwards problem solving process, we turned a hard problem of having 6L into a much easier one of having to get 1L from having 4 and 9 available; that’s kid's math.

That's an example of how to solve problems by working backwards.

But it's just an example of a much more important principle.

By working backwards, you start on the right track. Instead of brainstorming a bunch of ideas that will lead nowhere, you reduce the search area where you solution might turn out to be.

That’s how you solve problems by working backwards. I hope this helps you with any problem you face ion your life.

Thank you very much for reading. See you tomorrow.

This transcript has been edited for clarity.

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