>
>If anyone gets that #5, let's see it! :)
>
I've got the answer to number 5 below.
These are good brain teasers. Thanks Erik. :-) D-man and
I have arrived at the same answers for all but three of them (numbers
3, 5 and 8).
Steve
For those who don't want to see the answers, here's some spoiler space...
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>
>>
>> 1. A snail is at the bottom of a well 30 feet deep. It can crawl upward 3
>> feet in one day, but at night (being the slimy bastard that he is) it slips
>> back 2 feet. How many days does it take the snail to crawl out of the well?
>
>The answer is 28 days. On the 27th day, the snail starts at 26 feet up,
>climbs to 29 feet up, and slips down to 27 feet up. On the 28th day, the
>snail starts at 27 feet up, climbs to 30 feet up, and gets out of the
>hole.
>
Yup, the number of days will always be 2 less than the number of
feet deep the well is (unless it's less than 3 in which case it's always one
day).
>> 2. There are 2 jars of equal capacity. The first jar there is one amoeba.
>> In the second jar there are two amoebas. An amoeba can reproduce itself in
>> the three minutes. It takes the two amoebas in the jar three hours to fill
>> the jar to capacity. How many minutes does it take the one amoeba in the
>> first jar to fill that jar to capacity?
>
>Three hours and three minutes. It takes the single amoeba three minutes
>to become two amoebas. And we already know how long it takes two amoebas
>to fill the jar to capacity - an additional three hours.
>
>> 3. A ship is at anchor. Over its side hangs a rope ladder with rungs a foot
>> apart. The tide rises at the rate of 8 inches per hour. At the end of six
>> hours, how many feet of the rope ladder will remain above water, assuming
>> that 8 feet were above water when the tide began to rise?
>
>I'm not sure of this one, but it sure seems like a trick question. I'm
>going to say 8 feet, because the tide has to go back down sometime. I
>just don't remember when that is, so this is rather likely to be really
>wrong.
>
It is a trick question. You got the answer right, but didn't give
a sufficient reason. A boat always floats at the same depth in the water,
so the ladder will always be 8 feet out of the water. :-) The boat just
rises with the tide. The anchor doesn't prevent the boat from rising with
the tide, just from moving too far laterally (an anchor generally gives
enough slack to allow the boat to rise and fall with the wave and tides).
>> 4. A race driver drove around a 6 mile track at 140 mph for three miles, 168
>> mph for 1 1/2 miles, and 210 mph for 1 1/2 miles. What was his average
>> speed for the entire 6 miles?
>
>Unless I missed something really obvious, it's 164.5 mph.
>
I agree, although it's not possible to accelerate from 140 to 168 or
210 mph without going through some speeds in between. But we're not given
any information about that sort of thing so I assumed (as you did) that
we should accept those values at face value.
>> 5. If you get this one, I want to know how! With my logic, I almost got
>> it....
>> Each day a man's wife meets him at the railroad station and drives him home.
>> One day he arrives at the station an hour early and begins to walk home
>> along the road his wife always takes. She meets him en route and takes him
>> the rest of the way home. Had he waited at the station, she would have
>> picked him up exactly on time. As it turned out, he reached his home twenty
>> minutes early. How many minutes did the man walk?
>
>ARGH! The one I didn't get. :(
>
The answer is 50 minutes. :)
This one seemed impossible to solve, at first, because of a
lack of information. But, it became simpler once I drew a timeline for
the events and realized some relationships between them. Also, it was
key to begin the timeline at zero when the man arrives at the station
(sixty minutes early).
Man Wife Wife Normal Wife and Normal
Arrives Leaves Picks Time of Train Man Arrive Time of
Station in car Up Man Arrival Home Early Getting Home
|------------|---------------|------------|-------------|----------------|
0 60 - N P 60 (60+N)-20 60 + N
OK, here goes:
N = The amount of time it takes the wife to make the drive to the train
station. She will leave N minutes before the train will normally
arrive (hence the 60 - N marker). And they would normally get home
N minutes after the train normally arrives (hence the 60 + N marker).
P = Marks the time at which the wife picks up the man. It also corresponds
to the amount of time the man walks (P - 0).
Then, the key is to realize that the amount of time the wife drove
to pick up the man is equal to the amount of time they spent driving home.
Once you have that relationship, then it's easy to create an equation from
the above timeline:
Time spent driving to Time spent driving
the point where wife = home after picking
picked up man up the man.
P - (60 - N) = ((60 + N) - 20) - P
Solving for P:
P - (60 - N) = ((60 + N) - 20) - P
P - 60 + N = 40 + N - P
2P = 100
P = 50
And that's it! Since P is the amount of time that the man walks
before his wife picks him up, the man walked 50 minutes.
Before I used the timeline above, I had a lot of trouble with mixing
up distances and times to get places and absolute times (like the time of
the train arrival). Once I put it all in units of time relative to when
the man arrived early, it was simplified greatly.
The interesting thing is we still don't have any idea how long the
wife drove (or how long it normally took her to drive). We were just able
to eliminate that variable and solve for the man's walking time.
>
>> 6. How many times does the digit 9 appear from 1 to 100?
>
>20. An easy question to get wrong if you answer too quickly.
>
Yeah, I almost did that.
>> 7. A genious came to a narrow railroad bridge and began to run across it.
>> He had crossed three eighths of the distance when a whistle behind him
>> warned of an approaching train. Being a genious, he instantly evaluated his
>> alternatives. If he were to run back to the beginning of the bridge at his
>> speed of 10 mph, he would leave the bridge at precisely the moment the train
>> entered it. If he kept running to the end of the bridge, the train would
>> reach him just as he left the bridge. At what speed was the train moving?
>
>This one's tricky. It takes a lot of alternate thinking. If the genius
>can get back to the beginning of the bridge just as the train gets there,
>then it stands to reason that he can also get to 6/8 of the way across at
>the same time (because it's the same distance.) Now, the genius could get
>from 3/8 across to all the way across just when the train would get
>across. Let's say he/she does this. Once the genius is 6/8 of the way
>across, the train is at the start of the bridge. So, the genius is going
>to cover 2/8 of the bridge in the same amount of time as the train is
>going to cover the whole bridge. Therefore, the train's speed is four
>times that of the genius, or...
>
> b)40 mph
>
Yup. This one took me a while since I wasn't thinking about it
in the right manner.
>> 8.C, G, Q are to F, V, R as T, X, H are to
>
>This one's designed for math people. For those of you that don't know
>what a mathematical ring is, imagine a regular analog clock. Now imagine
>that instead of the numbers 1-12, it has the letters A-Z, all evenly
>spaced. In time, adding 1 to 12 gives you 1 again. On this clock, adding
>1 to Z gives you A. So, to get from C to F is the same amount of distance
>as getting from T to W, and so forth, so the answer is...
>
>> c) W, M, I
>>
>>
>>
>>
>> 9 Complete the series: 2-4, 6-18
>
>This one's a Mike Bahr-ism in a mutated form. :) To get from the first
>element of one set to the second element of the same set, multiply by x.
>To get from the second element of the first set to the first element of
>the second set, add x. Now, increment x and do it again. So, 2*2 = 4,
>4+2 = 6, 6*3 = 18, 18+3 = 21, 21*4 = 84, and...
>
>> e). 21-84
>
I actually got an answer of (c) 10-40, but either one is a possible
pattern. I used a pattern of the difference between the first two numbers
is 4 (hence next first number is 10). And the second number is equal to
2 times the first one, then 3 times the first one, then 4 times the first
one (hence the second number being 40).
There may be other possible patterns too, I suppose.
>>
>> 10. Which one does not belong?
>> a). dada
>> b). abstract
>> c). cubist
>> d). dodecaphonic
>> e). pointillist
>
>a,b,c, and e are all types of (visual) art. Dodecaphonic means
>(literally) twelve sounds.
>
I have to admit that I didn't know what dodecaphonic meant, but I
did know the others were art forms so that left only (d) as being different.
Steve
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