**ANSWERS
TO QUESTIONS FROM THE SOOTHSAYER**

CLICK A FELIX FOR MORE GAMES

**
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**

**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.**

**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.**
**.**

**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!)**

**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**
**confusion.**

**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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**ANSWERS
TO MORE QUESTIONS**

**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