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## Question

I used to present this logic puzzle to students and co-workers.

Fact 1: 50% of traffic accidents that result in injuries and deaths are caused by a drunk driver.

Fact 2: Traffic injuries and deaths are bad.

What is the third fact that is needed to reach the conclusion?

This is a logic puzzle, I do not know the current statistics on drunk driving. They are not relevant to the solution.

Edit: I'm sorry, I seem to have put this in the wrong category. I don't see a way to move it.

Edited by Scott from Eagan

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Your first reason is given, and so is your second, so your 3rd statement is stating the conclusion and using the transitive property as your reason. That's all you need.

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Your first reason is given, and so is your second, so your 3rd statement is stating the conclusion and using the transitive property as your reason. That's all you need.

No, there is a third fact not yet on the table. Were it reversed, the conclusion would not hold.

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Maybe that 50% is higher than any other cause of death?

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most accidents are traffic ones

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No and no. but slightly warm.

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less than 50% of people drive drunk?

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Fact 3: Being the cause of a traffic injury or fatality is bad.

(Fact 2 may be considered a red herring as it is not needed in reaching the logical conclusion that drunk driving is bad.)

Edited by Dej Mar
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I used to present this logic puzzle to students and co-workers.

Fact 1: 50% of traffic accidents that result in injuries and deaths are caused by a drunk driver.

Fact 2: Traffic injuries and deaths are bad.

What is the third fact that is needed to reach the conclusion?

This is a logic puzzle, I do not know the current statistics on drunk driving. They are not relevant to the solution.

Edit: I'm sorry, I seem to have put this in the wrong category. I don't see a way to move it.

maybe.....

people drink too much??

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Fact 3: drunk drivers do drunk driving

Fact 1: 50% of traffic accidents that result in injuries and deaths are caused by a drunk driver.

Fact 2: Traffic injuries and deaths are bad.

If I assume fact 2 to be "All" Traffic Injuries are bad then combining with fact 1 : drunk driver causes/does something that is bad.

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less than 50% of people drive drunk?

Plainglazed nails it.

The key is the wording "drunk driver", not "drunk driving" in fact 1. If in fact 90% of all drivers were drunk, and facts 2 and 3 are true, then we should be buying drinks for the other 10%.

I like these kind of puzzles that cause us to include our built in biases without even realizing it.

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An alternate answer might be Fact 3) That all accidents resulting in injury or death which were caused by a drunk driver would not have happened had the driver been sober.

It's impossible to prove, but if we assumed it, it would fit the bill.

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Driving drunk causes traffic accidents. Truthfully, fact #1 isn't even necessary. The fact that accidents are caused by drunk drivers doesn't make driving drunk bad, driving drunk is only bad if driving drunk causes the accidents. Without that fact, the drunkenness of the driver is incidental.

Edited by jpar1983
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I would probably have to dispute that Plainglazed nailed it. It took me a few minutes to understand the point he/she was making, and I admire the simplicity of the logic, but it still requires another logical step to say that it was the drunk driving that caused the accidents. From plainglazed's statement you must infer that drunk driving caused the accidents, which would then lead to the conclusion that drunk driving is bad.

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Fact 1: 50% of traffic accidents that result in injuries and deaths are caused by a drunk driver.

Fact 2: Traffic injuries and deaths are bad.

There are X amount of traffic accidents that result in injuries and death in a given time frame.

Or that there are any...50% of zero is zero. If there are no accidents then drunk driving is not bad. The fact I have given is more to deterine the magnitude of bad.

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Drunk Drivers do all drunk driving!

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Plainglazed nails it.

The key is the wording "drunk driver", not "drunk driving" in fact 1. If in fact 90% of all drivers were drunk, and facts 2 and 3 are true, then we should be buying drinks for the other 10%.

I like these kind of puzzles that cause us to include our built in biases without even realizing it.

I disagree. You can not logically conclude that drunk driving is bad from the three facts. Nor can you conclude that,

if in fact 90% of all drivers were drunk, and facts 2 and 3 are true, then we should be buying drinks for the other 10%. (I believe you have a built in bias, without realizing it.)

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There is a built-in assumption that the only important or salient property of drivers is whether they are drunk or not. All other factors affecting drivers and their propensity towards causing accidents are ignored for the sake of simplicity -- but that is not mentioned in the 'Facts'.

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I would probably have to dispute that Plainglazed nailed it. It took me a few minutes to understand the point he/she was making, and I admire the simplicity of the logic, but it still requires another logical step to say that it was the drunk driving that caused the accidents. From plainglazed's statement you must infer that drunk driving caused the accidents, which would then lead to the conclusion that drunk driving is bad.

You make a good point that the entire puzzle is based on what we infer, and it is not a logical proof. Several others have made similar observations. Tough crowd! By nailed it, I meant he hit the answer I was looking for. Perhaps it would be better stated as "What additional fact do we need to reasonably infer the conclusion that drunk driving is bad."

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fact 3 :drunk driving is bad

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Drunk driving leads to traffic accident that cause injuries and deaths.

Actually I don't think Fact 1 contribute anything essential to the conclusion.

If Fact 1 must be involved, then Fact 3 is: all drunk drivings contribute to the 50% of accidents in Fact 1.

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Bummer, I got here late.

If you said that 50% of accidents were caused by drivers wearing stupid hats, you would have to add that wearing stupid hats caused the accidents.

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Bummer, I got here late.

If you said that 50% of accidents were caused by drivers wearing stupid hats, you would have to add that wearing stupid hats caused the accidents.

I don't get why what you're saying differs much from

Fact 1: 50% of traffic accidents that result in injuries and deaths are caused by a drunk driver.

I think one can safely infer that the fact that the driver is drunk caused the accidents...even if not the statement "Drunk driving leads to traffic accident that cause injuries and deaths" doesn't add much more. For example how often do they occur? How does that differ from sober driving? What does leads to mean?

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I don't get why what you're saying differs much from

Fact 1: 50% of traffic accidents that result in injuries and deaths are caused by a drunk driver.

I think one can safely infer that the fact that the driver is drunk caused the accidents...even if not the statement "Drunk driving leads to traffic accident that cause injuries and deaths" doesn't add much more. For example how often do they occur? How does that differ from sober driving? What does leads to mean?

Let me put it this way. If fact 1 said 50% of traffic accidents that result in injuries or death are caused by a blonde driver, you would not infer that blonde driving caused the accident. (Well, I might, but it wouldn't be logical.)

I agree with you that it matters how it differs from sober driving, (or from brunette or redhead driving). The fact that we know being drunk impairs our reflexes and judgement really plays no part in a strictly logical argument.

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I reread your statement about stupid hats and it made more sense than the statement I quoted. Of course we already have a bias regarding the "badness" of drunk driving vs stupid hat driving.

I really think we just need one fact...something along the lines of

Drivers who drive while drunk are X times more likely to be involved in a fatal accident than those who are sober. (I guess from a logical standpoint we should add that this is a bad thing)

Edit- I'll test it prejudice free

People who drive while wearing a propeller hat are 15 times more likely to be involved in a fatal accident than those who drive with a fedora. Fatal accidents are bad. Driving while wearing a propeller hat is bad.

Edited by maurice
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I reread your statement about stupid hats and it made more sense than the statement I quoted. Of course we already have a bias regarding the "badness" of drunk driving vs stupid hat driving.

I really think we just need one fact...something along the lines of

Drivers who drive while drunk are X times more likely to be involved in a fatal accident than those who are sober. (I guess from a logical standpoint we should add that this is a bad thing)

Edit- I'll test it prejudice free

People who drive while wearing a propeller hat are 15 times more likely to be involved in a fatal accident than those who drive with a fedora. Fatal accidents are bad. Driving while wearing a propeller hat is bad.

So where's the flaw in

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