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Save the red flowers

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.


Puzzle ID:#12704
Fun:*** (2.36)
Difficulty:*** (2.93)
Submitted By:kvakk**
Corrected By:boodler




Hi. My name is Mister Kvakk. I live in a very big house in the country. Outside my house I have a lot of big gardens. In one of them I have ten beautiful, red flowers. These red flowers grow in a 5x2 rectangular shape:
The flowers had always lived in peace in this garden, until the day I allowed my stupid dog to go into the garden. This dog has only one goal in its life: it wants to eat as many red flowers as possible.
But the flowers are not normal flowers. They can think, and are able to talk to each other. And they now need a good plan to be able to save as many flower-lives as possible.
Each of the ten red flowers has the option to develop poison. If the dog is so unlucky to eat a poisonous flower it will surely die, and thus cannot eat any more flowers. So, when the dog arrives in the garden, it will start to eat flowers in random order as long as it is alive (the dog cannot see which flowers contain poison). If none of the flowers make poison, the dog will certainly eat all of them.
But how many flowers should make poison? Unfortunately, it's not possible to save every flower. The problem is that the creation of poison is a hard task to do. When one flower develops poison, it will use all the food and water that is in the ground around it. This will kill the flower to the left (if there is a flower to the left).
The flowers are not sure about how many flowers should make poison. They think that maybe only the two flowers to the very left should do it, but they are not sure. Therefore, they need your help.

Question 1: What is the maximum number of flowers that without risk can be guaranteed to survive?

Question 2: The flowers are risk neutral, and want to minimize the expected number of dead flowers. How many flowers should make poison to afford this?

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Jun 03, 2003

very difficult and very interesting
Jun 09, 2003

I thought this was really clever! It quite hard and i had to think for ages to get the answers!
Jun 09, 2003

I love your teasers! You fun rating should be a lot higher than what it is.
Jun 19, 2003

Yes, the expectation model is applicable, and has been put to good use. The case is not infinitely projectable, and so thanks for giving the numeric solutions!!
Feb 26, 2004

your answer is VERY wrong. the gog only eats red flowers, right? well dogs are color blind, so, depending on the size of the garden, then the chance of the dog eating a red flower lower dramatically. just thought you you'd like to know, good teaser nonetheless
(user deleted)
May 12, 2004

Well, sure, but it was still an awesome teaser.
Aug 01, 2004

The question is, which of the six potential suicide candidates will be killed by the flowers? Hopefully a volunteer.
Jan 10, 2006

I suddenly feel like a complete peabrain. I haven got a clue how to even approach this one.
Dec 15, 2008

I did it by calculating the expected number of survivors instead of expected casualties, but got the some probabilities.

I thought it was interesting, and somewhat unexpected, that the probabilities for 2 (no sacrifices) to 4 (2 sacrifices) were so similar. With the small population, my intuition was that sacrificing a flower would have had a larger effect on the probability.
Feb 20, 2009

My answer was to have all the flowers turn which way they are facing, so that "to their left" was always a spot that is currently empty!

Just kidding, I understood what you meant. This was a good puzzle and a fun presentation.

By the way, in reference to an earlier comment about dogs being color-blind. Not all dogs are -- there are breeds that can see some colors.
Nov 20, 2009

I dont know enough Math to complete the problem. Furthermore, es much as I love all types of Teaser, hard questions should be reserved in another section of
Braingle. And, reserve this section for the Fun Stuff. I know Math can be and is Fun for many people, but this Teaser just put damper in my funnybone.
A Teaser...

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