The lilly pad puzzle

The lilly pad puzzle

Imagine a small pond that has clear blue water reflecting the summer sky.

In the centre of the pond are two Lilly pads, the emergent leaves of an aquatic plant, floating safely on the surface of the water, curled up edges keeping the surface of the leaf dry.

On one Lilly pad is a green frog.

The frog is hard to pick out on the green pad but a yellow stripe on its back gives it away.

Chance happens that a week later you pass by the same pond and stop to admire the scene. Sure enough, the frog is still there only you notice that there are now four Lilly pads; the number of leaves has doubled. In a week the frog has gained surface real estate.

A week later you happen to pass by the pond again and even before you spot the frog you see that there are now eight Lilly pads. These aquatic plants are quite prolific.

You have to go away for a while and forget the frog and his growing number of Lilly pads. A few months pass. Delighted to return home you saunter by the pond again. The first thing you see is that the pond is now mostly green as half of it is covered with Lilly pads and rather less of the blue sky is reflected in the water.

Sure enough the frog is still sitting proud in the middle.

The puzzle question is this.

How many more weeks until the pond is completely covered with Lilly pads and the frog can hop to shore without getting wet?

The Lilly pad puzzle answer is…

One week.

When the pond is half covered with Lilly pads and they are doubling every week, the pond will go from being half covered with Lilly pads to totally covered in just one week. It is the reality of doubling.

Two to four seems like nothing much. Four to eight is mostly trivial too. But when the number is large and the doubling time short, then it is a different thing.

3,500,000,000 is a large number.

It happens to be the number of people on earth in 1967 just 44 years ago. Since then the human population has doubled to 7,000,000,000 (7 billion).

Unlike the pond, we cannot make the Earth any bigger that it already is. So we must hope that should the population double again, there is space enough.

The cute animal postscript

Hans Rosling explains why the human population is unlikely to double again. There are demographics at play that will see family size decline as kids survive better in the poorer countries and most of the world passes through the demographic transition.

But 12 billion people is a distinct possibility.