Water lilies

This caught many out with a considerable number of solutions suggesting that the answer was eight and a half days... but we had an even larger number of responses offering the correct solution:

Arran from Parkside Community College wrote:

It must have taken 16 days to fill half the pond because on the 17th day it doubled to cover all of the lake.

Matthew from Costessey High School added:

The number of lillies doubles every day. The lake is covered on day 17, so it must have been half covered the day before. That means it took 16 days for them to cover half the lake.

Emily from Dame Alice Owen's School wrote:

16 days - if the area of lillies doubles every day, then the number of lillies on the 17th day will be double the number on the 16th. Working backwards from this, there will be half the area of lillies on the 16th day than there will be on the 17th.

Will from SGS wrote:

If the water lilies doubles in size everyday, and on the seventeenth day it is fully covered, then when the water lillies were on the sixteenth day, the were covering half the pond.

If you try to work it out:

asssume that x is the pond fully covered with water lillies.

the sixteenth day = 1/2x

the seventeenth day = 1/2x * 2 = x

This works out to be the same answer as the question.

Alan from Hutchesons Grammar School added:

The whole lake is covered in 17 days and the area doubles every day, it must halve going back in the days

e.g. 17th day: 1/1

16th day: 1/2

15th day: 1/4

14th day: 1/8 etc

Therefore, half the lake is covered in 16 days, as the whole was covered in 17.

Cara from Platteville High School went about it differently:

I made a chart starting with any number at day one and then multiplied by two for everyday. At the end I took the last number and divided by two to find out what half would be and found out that it covered the lake on the 16th day.

Well done to you all.