# Christmas Sprouts Puzzle

After a short Christmas break, we are back and just creep into the twelve days of Christmas with a puzzle based on sprouts. We know some people love them and some people hate them, but we think you will like this puzzle to wake up the grey matter.

Two farmers met in the pub after a Christmas farmers’ market and started discussing the day’s trade.

“I sold all my sprouts” said the first, “every last one of them”.

“That’s good” replied his friend, “how many did you bring?”

“That’s the odd thing, I can’t remember. But I do remember that in the first hour I sold six sevenths of the sprouts that I brought, plus a seventh of a sprout”

“It must have been awkward cutting a sprout  . . .”

“Don’t be daft, I don’t cut them! And strangely, the pattern repeated itself. In the second hour I sold six sevenths of the sprouts I had left, plus a seventh of a sprout. Then in the third hour I sold six sevenths of the sprouts I had left, plus a seventh of a sprout. And finally in the fourth hour I sold six sevenths of the sprouts I had left, plus a seventh of a sprout. Then I came to the pub because I had no more sprouts”.

How many sprouts did the farmer bring to market?

And for those who like a bit more of a challenge – can you work out a general formula for the number of sprouts if this had gone on for five, six, seven hours or more?