Quiz/Brainteaser

We now have a weekly What Is It? blog, which is pretty entertaining.

I think you are remembering the monthly Challenge Questions.

Omnib0mb3r,

That's quite a clever brain teaser in itself. I give up. I have no clue.

Please PM the answer to me.

I will not reveal it to anyone.

Good Luck.

I'll take a shot with 'OmniBomber'.

Omni bomber?

Hmmm, kinda scary!

Here's a riddle for you:

I am weightless, but you can see me. Put me in a bucket, and I'll make it lighter. What am I?

You, Mizuti, are a hole (not a comment about you, that's my response to your riddle).

The equation shown below is not correct:
26-63=1
Can you make the equation correct by moving just one symbol?

Yes, I can:

2⁶-63=1

How many times a day does a clock's hands overlap?

EDIT: Don't use google!

The hands of an analog clock overlap every 65 minutes (+/-)... two trips around for the hour hand in one day... 22 times in 24 hours.

What's a Google? You're not the first guy to give me a pop quiz!

If the probability of observing a car in 30 minutes on a highway is 0.95, what is the probability of observing a car in 10 minutes (assuming constant default probability)?

Exactly one car, or at least one car?

Somebody else join in... I do have to do a little bit of work today!

0.95 is the probability for 1 or more cars, not the probability of seeing just one car.

What's the probability of seeing at least one car.

I can't see any cars from here.

<splarf>
Del

Okay, got that customer fixed up... back top the important stuff

Well, the probability of seeing NO cars in 30 minutes is 0.05, so the probability of seeing no cars in 1/3 of that time is the cube root of 0.05.

Probability of seeing at least one car in 10 minutes is 1-(0.05^1/3), ≈ .63

There is a number less than 3000 that when divided by 2 leaves a remainder of 1, when divided by 3 leaves a remainder of 2, when divided by 4 leaves a remainder of 3, When divided by 5 leaves a remainder of 4, when divided by 6 leaves a remainder of 5, and so on up to nine.

What is that number?

Let's find the least common multiple, and see if it's less than 3K.

N+1 must be a multiple of 2
N+1 must be a multiple of 4, but if a multiple of 2 and 4 it is a multiple of 8
N+1 must be a multiple of 5
N+1 must be a multiple of 6, but if multiple of 2 and 9 it's already a multiple of 6
N+1 must be a multiple of 7
N+1 must be a multiple of 9, thus multiple of 3

2×4×5×7×9=N+1= 2,520; Thus N = 2,519

Looks good from here. I see it works for 10 as well, remainder of 9.

How much wood would a woodchuck chuck if a woodchuck could chuck wood?

How many times does the letter 'F' -either in
upper or lower case-appear in the following
sentence:

Finished files are the result of years of
of scientific study combined with the
experience of years.

This, a slight variation of an old favorite.

Only two 'F's is the answer.

The instructions are asking about the 'f's in the sentence that follows, but a colon does not complete a sentence, so the sentence in bold is still part of the same original sentence, so it can't be considered the 'following sentence'.

The last remaining sentence has only two 'f's.

5

Nope, not 5:

Finished files are the result of years of
of scientific study combined with the
experience of years.

Note the double appearance of the the word of, ending and beginning a line.
I had this one on an aptitude test... yikes, who looks for typos in an aptitude test? Not a typo, part of the test.

A woodchuck would chuck all the wood he could chuck,

if a woodchuck could chuck wood.

That's one answer; however, I like to believe it is actually 361.923 cubic centimeters a day, if only because it sounds more pretentious

_Sauce

Was that an African or European woodchuck?

As much as he could, if he would.

Just as much wood as a woodchuck could, if a woodchuck could chuck wood.

1259

Doesn't work for 8. Leaves a remainder of 3.

right you are.... yours is the only under 3000 then.

I believe you are correct about #19. And I thought I was such a smarty-pants!

Light

Hmm, I suppose if you define "lighter" as "having more light" then yes, that'd be a correct answer as well!

Traditionally, the answer to the riddle is "a hole".

Space

You are in a row boat.

.

The row boat is floating in the pool that is 10ft long by 20ft wide by 5 feet deep. The boat is floating freely not touching any side nor the bottom.

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The waterline on the boat at current level as well as a few inches above and below creates a rectangle 4 ft wide by 6 ft long. Your highly adept sense of balance enables you to stabilize and level the boat to maintain the waterline dimensions within a minute or so after any changes.

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With you, in the floating row boat is a bowling ball 8 inches in diameter (with no finger holes) weighing 16 lbs.

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The (liquid) water, row boat, bowling ball and you are all very close to the same temperature.

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Because this brain teaser has taken so long to set up, making your time at pool unbearably long, you have become dehydrated (even though the pool is filled with pure deionized water, which you could have consumed) and less than perfectly rational. You suddenly feel outraged that there are no holes drilled in the bowling ball, and decide it should be tossed overboard.

.As you are sending the bowling ball overboard, the boat gets a bit tippy, and takes on exactly 16 pounds of water as you send the ball over. You and the row boat recover and the ball sinks to the bottom.

.

Part 1

When the water is again calm, and neglecting any evaporation or precipitation, is the water level in the pool higher or lower now than it was before you threw the bowling ball into the pool.

Part 2

How much does the water level change?

Well, I guess I'll play if nobody else wants to.

Volume of 16 lb ball is 269 in³. Volume of 16 lb of water is 443 in³. So a 16 pound swap will reduce the volume of water in the pool by 174 in³. The boat displacement will not increase and does not come into play here, so the pool level will drop.

How much? 174 in³ of water over 200 ft² is a depth of .006 in. So... not very much.

Flawless.

Flawless?...yeeeeahhh...ooh....almost!. The volume of the 8" diameter bowling ball is not 269 in³!

I'm just being a dink but think about it carefully for a sec. Somethin' is missing! _{(that's a hint)}

A solid sphere with no holes drilled (as specified twice in the original problem) has a volume of

(4pi/3)*r^3

A radius of 4 gives a calculated volume of 268.08257310.... which technically should round down to 268, but some conventions always round up and since this teaser was related to concepts not rounding, I deemed 269 to be well with spec.

Doh!!...I missed the no holes part. Twice!

I'll go sit in the corner now. :-(

Actually, when I first read your comment it made me kind of panic.

I recalculated but made an error in my calculation, using the diameter instead of the radius for the volume of the bowling ball (which made me think my original error had been only squaring instead of cubing to get volume, so I thought your hint of something missing referred to cubing versus squaring).

At that point I calculated the volume of the ball to be too large to sink, and thought I had screwed up royally by providing an unsolvable problem (since I specified the ball would sink). I don't know why this type of thing gets to me so easily, but I was red faced, hating the idea that I hadn't checked calculations better.

It took me a while to figure out what I had done wrong, and that it was originally correct. Amazing how far I can run astray with just the slightest encouragement..

I think the reasons that some may take you to task is simply your obvious rounding error, totally unnecessary, conceptual or not.

I was taught that up to 0.5, but not including 0.5, you rounded down. Everything above 0.5, including 0.5 was rounded up, unless otherwise stated in the rules, assuming that rounding is allowed at all.....

Therefore 268.08257310 (assuming this value is accurate, I did not check) should have been rounded down......or was there a statement somewhere that said it had to be rounded up.

If it had been for example 268.825731, then rounding up would have been correct.

Sorry, but your rounding up is not accurate enough for standard math....

PS. Its strange that you had a trailing "0", why was that? Had you already removed some values? (not that it would make any difference to rounding up/down before the decimal point....)

You and I share the same rounding convention.

Here is what is going on:

I created a variant of a brain teaser I appreciated some time ago.

It was barely light work for Doorman who gave a solid explanation for detailing how he arrived at the answer.

The teaser was not about rounding conventions nor calculator proficiency. It was about buoyancy. His calculation of volume for the bowling ball was 269 in^3 when the calculation before reducing to significant digits would be approximately 168.082573.....

It would have been petty for me to refuse to commend his solution, holding something back on the grounds of rounding errors. Who knows maybe he approximates pi at 3.142.

In fact insisting on 168 would have been incorrect. In the problem I believe I actually only specified the ball had a diameter of 8 inches. not 8.0 not 8.00 so 200 would have been the reported amount, if it were asked for.

But in fact, that was not the requested calculation....and since additional error is introduced if you perform multiple rounding-to-significance processes along the way instead of just one at the end, it wouldn't have been a reasonable criticism for me to make.

Ultimately the final answer is not changed when it is reported in significant digits.

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You are correct the trailing zero was a result of stopping before the entire reported series was complete.

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Even though we share the same convention for rounding to significant digits, I have to disagree with your dismissal of the 'always round up' convention as not being accurate enough for standard math (of course I don't know your definition of 'standard').

There are several examples for which rounding-up is not just acceptable, it is necessary. the two areas immediately come to mind. Number theory has several algorithms related to modular arithmetic that necessitate rounding up. Statistics is another field for which in certain areas rounding up is the rule.

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I came back to edit this in because I thought of another one.... When calculating the minimum requirement for something, it is certainly accurate enough for standard math to round up to the next integer. Doing otherwise would be wrong. Example: minimum number of divisions required to use simpson's rule for an equation with error bound to <=0.0001....... n must be an integer and any rounding must be done upwards (it also has to be even if I remember right)

I did not see anywhere here where specific rules for rounding up/down were promulgated/specified.

Other rules can apply when specified as you point out, but they weren't specified here....

So standard rules apply.....its really that simple.

In standard rounding convention with which you and I are familiar, if 269 is incorrect, what do you propose in its place...given it is not a requested answer and that this is an informal conversation?

.

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(in the interest of lively debate, I'm setting aside a commonly adhered to rule stipulating 'the person who offers the challenge, picks the winner')

(on another note, don't hold your breathe waiting for someone to specify rounding-up when dealing with something like minimum necessary divisions for error bound calculations or minimum required people. It won't be specified on a per incidence basis as it is never specified in any other way.

Here is a link showing the three most basic rules of rounding, usually the first two are most commonly used:-

Rounding

I believe this is what you were looking for and if I can assist further just ask.

Hi guys... I have some observations about the puzzle from tinac, and my subsequent offered solution.

The questions, after the narrative:
When the water is again calm, and neglecting any evaporation or precipitation, is the water level in the pool higher or lower now than it was before you threw the bowling ball into the pool.
Part 2
How much does the water level change?

The question ...is the water level in the pool higher or lower. was answered. Could have been a guess, had a 50/50 shot at this one.

The question How much does the water level change? was also answered, but my less that exact "Not very much" could use some expansion, demonstrating the problem was understood and solved rather than some wild arsed lucky guess.

I expected more grief over volume of 16 lb of water is 443 in³. That is correct (enough) for 4° C, not 32° C (human skin temp, more or less), which was alluded in the narrative.

OK

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The answer you provided was correct and accurate to the appropriate number of significant digits. The explanation of concepts was correct in all that it described. The level of analysis was appropriate given the explanation and the accuracy of the data provided.

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I deemed that worthy of recognition as the right answer. In retrospect, at the insistence of now three separate protest, I beginning to understand my folly. My mistake was using calculation of a specific example eliminate guessing, but not following through with sufficient rigor once it had been established that the answer was based on correct analysis.

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The criticisms are fair: even though the concepts are correct, every error, no matter how small has a chance to induce much larger significant error once a convention for rounding to significant digits is employed.

For example, when answers are to be reported to one significant digit, an error causing about a 1% reduction in the calculated final value before rounding (like the error introduced in the problem in question be using a volume based on a lower temperature), will cause no variation in the reported answer roughly 94% of the time. But when it does result in error, the error is large; at least low by 10% and possibly by as much as 50%.

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The funny thing is that because of rounding conventions, for small errors ( smaller than 0.5/10^(number significant digits)) the percent variation in the as-rounded final answer, does not depend on the size of the error.

For example, in the flawed brain teaser i proposed, although the size an error which results in a lower before rounding calculated value does affect the likelihood that it will result in a different final rounded answer, because the final answer should be reported with only one significant digit, any error less than -5% that changes the rounded final answer, will result in an answer that is at least 10% low, and possibly 50% low.

Depending on the problem and even the units used, it is entirely possible that a seemingly insignificant variation of 0.0000000000000000000001% could result in answer that differed by at least 10% and up to 100%.

For example for answers with one significant digit if a pre rounded calculation is 1.499999999999999999999 after accounting for a very small effect but 1.500000000000000000000 before, once rounded to significant digits, failure to account for the effect results in a reported value 100% higher than if the effect is account for.

...

...

Which brings me back to the point. The inclusion or exclusion of incredibly small effects can influence answers (rounded to significant figures) to a degree far in excess of the relative influence on the problem as a whole.

This suggests that no influence no matter how small can be unequivocally deemed too small to affect an outcome.

In that case, given the vast number of possible (even though exceedingly small) influences, no analysis could be considered reasonably complete, unless....and this is the strange part... units can be utilized that yield an answer that is further away from any rounding mid point than the estimated maximum possible net effect of the remaining (not calculated) influences.

Does anyone do this? How do you get a decent idea of the remaining influences without falling prey to the self deception that you are cognizant of all possible influences?

As an example, in a situation similar to the brainteaser I presented, if the before-rounding answer (as calculated with consideration of all influences normally deemed of significance) were sufficiently close to a point where rounding changes from down to up, 6.499999999999999999999999999999999999999 for example, doesn't this necessitate taking into consideration a number of new previously overlooked influences?

- When the ball is dropped into the water and sinks to the bottom, this is a conversion of gravitational potential energy ultimately mostly into heat. This should cause a decrease in the water density (and bowling ball density) resulting in a different answer.

- Because the center of mass of the system lower at the end of the problem than the beginning, all other things being equal, the earth should spin slightly faster, decreasing the pressure felt by the water below from the water above, the small pressure coefficient of density would result in a very small increase in volume.

- There are no details about the draft of the rowboat or the particulars as to whether the rowboat lacks a scalloped keel which is likely to rest upon and transfer weight to the sunken bowling ball, yet floated free before it was cast overboard. While we might consider this very unlikely, even with a very low probability, the significant difference in end result should warrant consideration, given the very small effects of the things considered above.

.

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As a result. i am declaring all people who attempt to answer or discuss the brain teaser to be wrong, including myself. Furthermore, as a person cannot be wrong if they provide the right answer, since all people are wrong, by necessity all answers are wrong. Ergo sum the question is moot.

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Just one further note:

'.....The question ...is the water level in the pool higher or lower. was answered. Could have been a guess, had a 50/50 shot at this one......'

Actually there are three final conditions and so three possible answers to the question: higher, lower, neither.

I worded the question this way in hopes readers would notice my failure to mention the third option, and think I was attempting to obscure the correct answer; as many people initially think the water level is unchanged.

By the way this is not an unfair question. Technically, 'Is the water level in the pool higher or lower' is properly answered with 'yes' or 'no'. If one were intending to elicit 'higher' or 'lower' as answers, one solution would be to ask 'would the water level be higher or would the water level be lower.'

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Brain teasers are too much work.

If a plane crashes on exactly the Utah/Kansas border, then in which state do they bury the survivors?

Why would you bury survivors?

Very good, but there is no Utah/Kansas border.

Nice twist to an oldy.

They usually let them go home......

If you where placed in a room with no doors and no windows. (like you where beamed into an indestructible titanium cube), and all that is in the room is a table and mirror. How do you get out?

This is a riddle I give to get my students to start them thinking out of the box. (pun intended)

Not really a riddle. It's a play on words. Look in the mirror and see what you saw. Take saw and cut table in half. Put two halves together to make a whole. Crawl out the hole.

I've always found this one silly because it has no basis in reality.

You also can't mention "indestructible titanium cube" because then you could't make a hole in it. Right?

Good job TerraMan, where had you heard this before? Yes, it is a play on words.

A "riddle" is defined as "a misleading question" which a play on words is misleading.

Also of note: Reality is a matter of perception, until you learn otherwise what is real. It used to be the world was square, until we learned a new reality. The Higgs - famously dubbed "the God particle," was only a theory, until they recently proved it, now it is reality.

The only true reality is that none of us will really know if it is real... we can only believe until something else in the infinate universe comes along to prove otherwise. he he

"...where had you heard this before?"...University professor. Long time ago. I did not figure out the answer the first time I heard it. Way too "out of the box" for me.

You're right about reality. Depending on my mood, I often choose to substitute it with my own version!

Joseph was terrified of the dark and of the Nightmare Werewolf, whom he feared would catch him out of bed in the dark. When Joseph went to bed, he would flip off the light switch on the far wall, then dash across the room to bed, 13 feet away.

However, yesterday he flipped the switch, walked slowly to his bed, and climbed in without a worry. Without using anything other than his finger to flip the switch, how did he manage to do this so calmly?

He went to bed while the sun was still up.

Sort of a big bedroom for a kid, isn't it?

Kids today are spoiled.

Many miles away, a hunter left his camp early in the morning and tracked a bear due south for 10 kilometers. At this point the bear turned due west and went another 10 kilometers before the hunter caught up with him and shot him dead. The hunter then dragged the carcass of the bear back to his camp, a journey of exactly 10 kilometers. Given these facts can you tell me what colour the bear was?

Oh, come on... That's not how to spell 'color'.

Aha! You've given a hint, allowing a me deduction.

There are no bears in Great Britain, but there are many deciduous trees and deciduous trees have leaves. There is a British musician, a mandolin player named Leafcutter John, who plays for an experimental jazz band named Polar Bear and as everyone knows a Polar Bear is white.

I have no idea what this has to do with your puzzle, but an amazing deduction, eh?

Wow!...You're like this guy!

White?

He switched the light on?

The location is the north pole and yes the bear would be white .