# The doubling lily pond: visual puzzle and solution | SwaVid

A patch of lily pads doubles in area every day. It completely covers the pond today. When was the pond exactly half covered?

Canonical: https://www.swavid.com/puzzles/quiz-2

Source: https://www.swavid.com/puzzles/quiz-2

# The doubling lily pond

## The pond was half covered yesterday.

### Name today’s coverage

### Reverse one doubling

### Locate the half-full day

SwaVid visual puzzle

A patch of lily pads doubles in area every day. It completely covers the pond today. When was the pond exactly half covered?

Detailed solution

Doubling works backwards too: the amount immediately before a full pond must be half a pond.

Today the lily pads cover one whole pond, which is 100% of its surface.

To find the previous day, divide today’s coverage by 2 because the patch doubles from one day to the next.

The previous day is yesterday, so yesterday’s 50% coverage doubled to become today’s 100% coverage.

It is tempting to guess the middle of the total growth time. Exponential growth is not evenly spread: half-full occurs just one doubling before full.

- 1 Name today’s coverage Today the lily pads cover one whole pond, which is 100% of its surface. Today = 100%
- 2 Reverse one doubling To find the previous day, divide today’s coverage by 2 because the patch doubles from one day to the next. 100% ÷ 2 = 50%
- 3 Locate the half-full day The previous day is yesterday, so yesterday’s 50% coverage doubled to become today’s 100% coverage. 50% × 2 = 100%

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