Today Puzzle #707
Puzzle No. 707鈥� Tuesday 31 March 2020
Bert and Carole found some time to plant their rhubarb plants. They have nineteen rhubarb plants, and they would like to plant them in an arrangement so that
a. The arrangement consists of 9 straight lines, and,
b. on each of those lines, there are exactly 5 rhubarb plants.
Can they do it?
Today’s #PuzzleForToday has been set by Dr Nicos Georgiou, a senior mathematics lecturer from the University of Sussex.
Click here for the answer
This is possible. One way this can be achieved is the following: Consider a regular hexagon (a hexagon with all sides equal and all angles equal); we just want the 6 corner points. Now draw all lines connecting any two points that are not next to each other (this creates a star). There are precisely 9 such lines.
At every point of intersection of these lines (these include the corners of the hexagon) they should plant a rhubarb plant. There are exactly 19 points of intersection, which is precisely the number of plants. And each line goes through precisely 5 of these points, so each line will have exactly 5 plants on it.
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