An IQ test for fun

Here is an IQ test for fun. I answered 3 of 5 questions correctly. Let's see how well you guys (the advantage players) do. Have fun.

Below are five (5) questions. You have to answer them instantly. You can't take your time, answer all of them immediately. OK?

Let's find out just how clever you really are....

Ready? GO!!! (scroll down)

First Question:

You are participating in a race. You overtake the second person. What position are you in?
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Answer: If you answered that you are first, then you are
absolutely wrong! If you overtake the second person and you take his place, you are second!

Try not to screw up next time.
Now answer the second question,
but don't take as much time as you took for the first question, OK?

Second Question:
If you overtake the last person, then you are...?

(scroll down)

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Answer: If you answered that you are second to last, then you are wrong again. Tell me, how can you overtake the LAST Person (you were the last person)?

You're not very good at this, are you?

Third Question:
Very tricky arithmetic! Note: This must be done in your head only.
Do NOT use paper and pencil or a calculator. Try it.

Take 1000 and add 40 to it. Now add another 1000. Now add 30.
Add another 1000. Now add 20. Now add another 1000
Now add 10. What is the total?

Scroll down for answer.....

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Did you get 5000?

The correct answer is actually 4100.

If you don't believe it, check it with a calculator!
Today is definitely not your day, is it?
Maybe you'll get the last question right....
.....Maybe.

Fourth Question:

Mary's father has five daughters: 1. Nana, 2. Nene, 3. Nini,
4. Nono. What is the name of the fifth daughter?

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Did you Answer Nunu?
NO! Of course it isn't.
Her name is Mary. Read the question again!

Okay, now the final round:

A mute person goes into a shop and wants to buy a toothbrush. By
imitating the action of brushing his teeth he successfully
expresses himself to the shopkeeper and the purchase is
done.
Next, a blind man comes into the shop who wants to buy a pair of
sunglasses; how does HE indicate what he wants?

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He just has to open his mouth and ask... It's really very simple.... Like you!

Source: from a colleague's email.

I am currently hiring a number of people for the plant I manage. My boss has requested that I draft a reading comprehension and math test to evaluate applicants.

I edited out the answers of your test and gave it to him. At least I got the fourth and fifth answers correct which is two more correct answers than he got.

Thanks for the laugh.

-T-

Question 2 did not have a correct answer, as the premise was impossible. Apparently, the question does not allow the possibility that you join the race after it has begun, which is the only way that the situation could occur (and the correct answer in that case would be "second to last"). Other 4 questions were very straight forward.

This problem went around the web several years ago. It is simple
and accessible to anyone, but there were math Ph.D.s who got it
wrong and argued, wrongly, for months trying to save face.
Also, the thinking involved, I think, is related to the type
of thinking needed for skilled Blackjack play...

You are a contestant on the TV show, "Let's Make a Deal".
The host shows you three doors A,B,C; and promises that behind
one of the doors is the grand prize of a hot new car and a one
month tropical vacation including the beautiful hostess. Behind
the other two doors are booby prizes (nothing). You pick door A.
The host then opens door B and shows there was a booby prize
behind it. Then the hosts gives you the option to stick with
door A or change to door C.

QUESTION:
Is it best to switch to door C?
Or, does it not matter (probability the same) whether you
stay with A or switch to C?
Or, is it best to stay with A?

And why?

First, let me thank XXX for the original question. I have to confess that you caught me on the arithmetic problem. I got the other correct.

Regarding Barber�s Monty Hall problem: This problem goes back to the early 90s. There was a pop writer named Marylyn who was allegedly a Savant. She had a syndicated column that billed her as the world�s smartest person, or something.

She listed this problem, and gave the �correct� solution. She got a lot of flack for it, from some Ph.D�s. It caused quite a buzz. There was even an article in the ASA (American Statistical Association) journal about it. So far as I know, the ASA article is the only place where the genuinely correct solution has been printed.

I will say that I got it right the first time. Not only did I get the short �correct� answer, but I understood the lengthy answer.

And the full answer is: It depends on the policy used by the Game Show Host. (In the ASA article, this is called the Strategy). Depending on the policy:

It may be optimal to switch your choice
It may be optimal to hold your choice
It may not matter.

The specific policy that the Host is using is not spelled out the problem, and is open to interpretation. Many of the �wrong� solution are actually the correct analysis for certain policies.

There is an important point here: You should always make your assumptions explicit and understand the role of them in your solution. Some of the most common errors occur when people apply a result to a situation where it does not apply, because the assumptions have not been met.

To return to the Monty Hall problem, you may feel that there is only plausible interpretation. I think there is one natural interpretation, but a credible argument can be made for the others.

Your problem explicitly mentioned �Let us Make a Deal�. Other statements of the problem referred to it as the Monty Hall problem. In Marylyn�s original problem, it was a generic game-show.

It may be that the policy of the Host is obvious to viewers of that show. I say �may� because I don�t know; I don�t watch the show. I have seen it listed on my local PBS station.

If the Math Ph.D�s made a mistake because they did not watch that game on TV, then see that as a point in their favor : )

"Take 1000 and add 40 to it. Now add another 1000. Now add 30.
Add another 1000. Now add 20. Now add another 1000
Now add 10. What is the total?"

The answer could also be 3100 if you interpret the "Take 1000" in the first sentence as -1000.

problem:
-The car exists and does not move;
-The host does not know which door the car is behind.

I think the buzz about it may go back a little further than
the early 90's. I remember long arguments with my grad school
housemate, a chemistry PhD candidate. I was right, he was wrong,
it almost became violent.

Maybe all the math PhDs were crowded out of the TV show by all
the physics PhDs in then audience :-)