1.    In the order: "elder, younger", there are four possibilities before you get told the extra information, and all are
equally likely: "Boy,Boy" "Boy,Girl" "Girl,Boy" "Girl,Girl" Once you are told there are not two girls, you you can eliminate
the fourth possibility, which leaves three equally likely possibilities.  "Boy,Boy" "Boy,Girl" "Girl,Boy"
And of these three, the elder child is a boy in two cases, so the answer is two thirds.

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2.     In the order: "elder, younger", there are four possibilities before you see the child, and all are equally likely:
"Boy,Boy" "Boy,Girl" "Girl,Boy" "Girl,Girl"  It is tempting to say that once you discover one childis a boy you can eliminate
the fourth possibility, (like the previous question) which would leave three equally likely possibilities.
"Boy,Boy" "Boy,Girl" "Girl,Boy"  And so of these three, the other child is a boy in only one case, so the answer would be one
third.  But that isn't right. You have to ask yourself: "what are the odds of seeing a boy in the first place?"  On average, of
every eight people who look, there will be four pairs of people, and each pair will encounter one of:
"Boy,Boy" "Boy,Girl" "Girl,Boy" "Girl,Girl"  On average one of the pair will encounter the elder and one will encounter the younger.  Two of the eight will encounter a "Girl,Girl" family, and will not report a boy.  Two of the eight will encounter a
"Boy,Boy" family, and both will report a boy. Two of the eight will encounter a "Girl,Boy" family, and one will report a boy.
Two of the eight will encounter a "Boy,Girl" family, and one will report a boy. Of the four who report a boy, the other child will
be a boy in two cases and a girl in two cases, so the answer is one half

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3.    First note that since Monty Hall always opens an empty box, there is no chance to change strategy depending on what can
be seen inside, and so the contestant should choose a strategy consistently. Unless the strategies are equally good, the
contestant should either always "switch" or always "stick".  There are two ways of answering the question: the "arithmetic"
way and the "common sense" way.  The "arithmetic" way to answer the question is to look at how each strategy fares on
average.  With probability one third, a contestant will choose the correct door at the start. The sticker wins in this case, and
the switcher loses.  With probability two thirds, a contestant will choose the wrong door at the start.  The sticker loses in this
case, and the switcher wins.  So the sticker wins one third of the time, and the switcher wins two thirds of the time, so the
contestant should always switch.  Now for the "common sense" way: The sticker stays with his original choice, so his chance
of success is his original one third.  The switcher and the sticker would always choose different boxes, and there are only two
boxes, and just one box contains a prize, and so the switcher's chance of winning is the same as the  sticker's chance of losing:
two thirds.  So the contestant should always switch.

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4.    This was the soothsayer's prediction: "I predict that you will either execute me today or not at all."  He continued,
explaining that there were three choices the despot could make.  The first option was to kill the soothsayer the same day.
But in this case the soothsayer's prediction would be true, and so the despot could not kill him the same day without
breaking his promise.  So the despot couldn't do that.  The second option was to kill the soothsayer some day in the
future.  But in this case the soothsayer's prediction would be false, and so the despot would have to kill him the same
day instead, or else break his promise.  So the despot couldn't do that either.  The final option was not to kill the
soothsayer at all. In this case the soothsayer's prediction would be true, and so the despot either kill him (which we
have already excluded) or not kill him at all (and keep his promise).  So the despot could do that.

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5.     We can exclude no blue spots, because there is at least one.  If there were just one blue spot, then one child (the one
with the blue spot),  would only see yellow spots, and since there has to be one blue spot, it must be the one spot he can't
see - his own!  So he would yell out during the first round.  As there was silence during the first round, all the children now
know that there are at least two blue spots - otherwise the single blue spot child would have called out.   So now, any child
who saw just one blue spot would know that he had to have the second blue spot. So if there were two blue spots, two children
would call out in the second round.  And so on. With every round of silence, the whole class learns that they can eliminate
one more possible number of spots. For example after eleven rounds of silence,  all the children would know that there were
at least twelve blue spots, and so any child who saw eleven would answer in round twelve. The rule for each individual child
is simple. At the start he should count the number of blue spots he can see, and then he should wait for that number of rounds
of silence before shouting (assuming the game goes on that long!)

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Easy 1.  The Solution:The man was counting pins as he removed them from a  new shirt.  Unfortunately he missed one.

Easy 2.  The Solution:The truck driver was walking.

Easy 3.  The Solution:The fugitive leapt up and shouted, "Fire, fire!" Pandemonium broke out and he easily escaped in the

Easy 4.  The Solution:Two weeks later, when the couple returned from their honeymoon, the whole family sat down to watch
the video of the wedding.   They were horrified to see, caught on the camera, the groom going through his father-in-law's
pockets and stealing his wallet.

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Medium 1. The Solution:They spread out and waded across the river, which was only six inches deep.

Medium 2. The Solution:The place is Venus, where a day is longer than a year.

Medium 3. The Solution: They are all impostors. The koala bear is not a bear; it is a bear; it is a marsupial. The prairie dog
is not a dog; it is a rodent. The firefly is not a fly; it is a beetle.

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Hard 1.The Solution:He was an Indian brave who sent smoke signals alerting a war party to the approach of the cavalry troop.

Hard 2. The Solution:A new traffic regulation, designed to encourage car sharing, stated that only cars carrying two or more passengers could use certain lanes of the freeway. This led to motorists buying blow-up dolls to give the appearance that they
were carrying passengers.

Hard 3. The Solution:The criminal sent an invoice to a blind man who had recently died. His widow immediately knew that it
must be a scam.

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1. The man is very, very short and can only reach halfway up the elevator buttons. However, if it is raining then he will have
his umbrella with him and can press the higher buttons with it.

2. The surgeon was his mother.

3. It was day time.

4. At the time she went into labor, the mother of the twins was traveling by boat. The older twin, Terry, was born first early
on March 1st. The boat then crossed a time zone and Kerry, the younger twin, was born on February the 28th. Therefore,
the younger twin celebrates her birthday two days before her older brother.

5. A square manhole cover can be turned and dropped down the diagonal of the manhole. A round manhole cannot be
dropped down the manhole. So for safety and practicality, all manhole covers should be round.

6. The poison in the punch came from the ice cubes. When the man drank the punch, the ice was fully frozen. Gradually it
melted, poisoning the punch.

7. He recognized Adam and Eve as the only people without navels. Because they were not born of women, they had never
had umbilical cords and therefore they never had navels. This one seems perfectly logical but it can sometimes spark fierce
theological arguments.

8. They were two of a set of triplets (or quadruplets, etc.). This puzzle stumps many people. They try outlandish solutions
involving test-tube babies or surrogate mothers. Why does the brain search for complex solutions when there is a much
simpler one available?

9. The man had hiccups. The barman recognized this from his speech and drew the gun in order to give him a shock. It worked
and cured the hiccups--so the man no longer needed the water. This is a simple puzzle to state but a difficult one to solve. It is
a perfect example of a seemingly irrational and incongruous situation having a simple and complete explanation.  Amazingly
this classic puzzle seems to work in different cultures and languages.

This test does not measure intelligence, your fluency with words, creativity, or mathematical ability. It will, however, give
you some gauge of your mental flexibility.

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Optical Illusion
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Last edited on 5-25-2000