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Kiwifruit combos

By David, 19 February 2020 Brainteaser

Difficulty: Tricky

Chloe is researching kiwifruit. Kiwi plants are unusual compared to many plants, as they’re either male or female. To make a kiwifruit, you need pollen from a male plant to fertilise a flower on a female plant.

There are many different breeds of kiwifruit. Chloe wants to know the combination that produces the tastiest fruit, so she’s going to buy some different plants to do some cross-fertilising.

Female plants have many flowers that can each accept different pollen, and each male plant has enough pollen to fertilise lots of different flowers.

Chloe has enough money to buy 10 plants and wants fruit from as many combinations of male and female as possible.

How many male plants and how many female plants should she order?
 
Scroll down or click for a hint, or the answer!

 

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Brainteaser hint

To work out the total number of combinations in an order, multiply the number of male and female plants.

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Brainteaser answer

A good way to get a handle on this brainteaser is to try a few orders and see what you get!
• Nine female plants and one male gives you nine combinations
• Nine male and one female also makes nine combinations
Notice that swapping the numbers of male and female plants doesn’t affect the number of combinations.

We can work through all the other combinations quite easily:
• Eight female x two male plants = 16 combinations (imagine this as two different combinations on each female plant)
• Seven female x three male = 21 combinations
• Six female x four male = 24 combinations
• Five female x five male = 25 combinations

So, the best order is five female and five male plants!

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