The Garden

Logic Level 3

A garden contains flowers of three colors: green, yellow and red.

Fact 1: If you choose any three flowers from the garden, at least one of them will be green.
Fact 2: If you choose any three flowers from the garden, at least one of them will be yellow.

True or False?

If you choose any three flowers from the garden, at least one of them will be red.

True False Insufficient information

Denton Young by Denton Young , 47, USA

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1 solution

Denton Young
Oct 2, 2016

By fact 1, there is only one yellow and one red flower in the garden.

By fact 2, there is only one red and one green flower in the garden.

Therefore, the garden contains exactly one flower of each color. So there is only one way to choose three flowers from the garden, and that way includes a red flower.

10 Helpful 0 Interesting 0 Brilliant 0 Confused

It's a sad garden that only has three flowers, and once they are all picked, can we still call it a garden?

Tom Capizzi - 4 years, 8 months ago

the answer is wrong , who said the garden contains exactly one flower of each color. there may or may not be a red colored flower.

A Former Brilliant Member - 4 years, 8 months ago

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First line of the problem.

A garden contains flowers of three colors: green, yellow and red.

Denton Young - 4 years, 8 months ago

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But just because there are 3 different colors doesn't mean there are 3 flowers, you could only conclude that there are atleast 3 flowers

tahseen sarwar - 2 years, 5 months ago

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@Tahseen Sarwar – That's why we need Facts 1 and 2.

Denton Young - 2 years, 5 months ago

But the statement says atleast one red.... As there is exactly one red, the statement atleast one red is wrong!

Kunal Gupta - 4 years, 8 months ago

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Brush up on your logical rules. If I have "at least one" of something, that includes the possibility that I have exactly one of it. So since there is exactly one red flower if you pick three, there is also at least one red flower.

Denton Young - 4 years, 8 months ago

Is the statement "2 is greater than or equal to 1" true? I suppose so.

William Nathanael Supriadi - 4 years, 7 months ago

If you only have three flowers to pick from you are not 'choosing' the flowers to pick if you have to pick three - you are just picking all the flowers.

Chris Hallo - 4 years, 7 months ago

The garden consists of flowers of three colours so there can be many flowers. So from fact1 we cannot say there is only one yellow and one red flower in the garden! I think it should have been mentioned that there are only three flowers in the garden.

Nashita Rahman - 4 years, 8 months ago

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No, that shouldn't have been mentioned because it's what we need to figure out. And yes, from fact 1 we can actually say that there is only one yellow and one red flower. If there were more we could pick for example 3 flowers like this: 2 yellow and 1 red, or 1 yellow and two red which contains no green flowers and hence contradicts fact 1.

Kai Ott - 4 years, 8 months ago

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I got it now! Thanks .

Nashita Rahman - 4 years, 8 months ago

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