Math Riddle

Math Riddle
by capt_ayhab
27-Feb-2009
 

One late night three traveling businessmen arrive at a hotel in a small town and ask for a room for each. Innkeeper tells them since there is a convention going on in the town, there is only one vacant room available.

Men who were tired from a long flight, asked if they could share the room. Innkeeper accepts and tells them the price will be $30.00. Men chip in $10 each and go to the room to rest.

After they leave, the innkeeper realizes that he has over charged the men, since the usual rate of room for one night is only $25. He gives $5 to bellhop and asks him to take to the men as refund.

On his way to the room, knowing that he can not divide $5 between three men, keeps $2 and refunds$1 each to the guests. Travelers were happy since their share of one night in hotel was $9. each.

Quiz: Men originally paid $10 each, After the refund they each have paid $9[$10 - $1 =$9]. Calculation is as follows:

They paid ..... 3 x $9 = $27

Bellhop kept ............ $2

Total ................... $29

Initial pay.............. $30

Missing $ ................. $1  Where did $1 disappear??

 

Source: Unknown

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capt_ayhab

Horse Problem!

by capt_ayhab on

A man buys a horse for 50 dollars. Decides he wants to sell his horse later and gets 60 dollars. He then decides to buy it back again and paid 70 dollars. However, he could no longer keep it and he sold it for 80 dollars.

Did he make money? lose money? or break even? Explain why.

-YT

P/S blog e mano hijack mikoneen???? lol


Jaleho

mornin smart ladies and gents!

by Jaleho on

Maghshoosh jon,  when my daughter frustrated showed me the puzzle which she was working on for an hour, I looked at it and said: "yeah, just move that stick from equal sign to the negative and voila, just one move" She banged on my head (made me maghshooh) and shouted "you cheat!! it is a digit, not a thingie!"

Anyway, Foad got it right in base 10. But, I just loved your base 3 solution as it shows a different wiring of the brain, and as Irandokht said, not maghshoosh at all :-)

Agha Majid better come up with another puzzle. After Irandokht gave the essential start of dividing the balls into groups of 4 and eliminated the equal case, and Maghshoosh did the second tricky part, no one is going to bother to write it neatly! 

Thanks to all for the fun participation, and bring them on!


capt_ayhab

New One

by capt_ayhab on

Two fifty foot ropes are suspended from a forty foot ceiling, about twenty feet apart.

Armed with only a knife, how much of the rope can you steal?

-YT


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مجید آقا

JD (not verified)


مجید جان، اگر از اول اعلام کرده بودی که این معمای شما سرو کارش با اعداد باینری و ریاضیات روانکاوی و الهیات مربوط است، خوب ماشب جمعه ای میرفتیم بیرون اقلا یک نفسی بکشیم و این چند تا سلول سالم مانده مغز را اینقدر زیر کار نکشیم که کوفته شوند! و امروز کلی فکرم درد میکند.

هی نشستیم که جواب بیاد، آخرش هم که پاسخ آمد دیدیم خود جواب از سئوال بمراتب سخت تر است! آخه اینهم شد زندگی؟ حالا تو رو خدا یکی بیاد "پاسخ" این "جواب" را برای ما حل کنه و توضیح بده. دیگه اعصاب برایمان باقی نماند.


Foaad Khosmood

Jaleho, is it move the 2 to superscript?

by Foaad Khosmood on

like

 

101-102=1 


LanceRaheem

The amount to be reconciled should be based on $25, not $30

by LanceRaheem on

Room rate: $25 + $2 bell hop + $3 refund = $30

There is no missing dollar!  Unless of course one bases the amount to be ronciled on $30.

$30 - $27 ($9 paid by each man) -$2 bell hop = $1 mysteriously missing!


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Puzzled me out.

by maghshoosh (not verified) on

Jaleho, Your puzzle is wrapped in an enigma, which is surrounded by a mystery, i.e. dolmeh mo-amaa. You said moving only one "digit" around, but if that's interpreted as "character," then take one of the parallel lines from the "=" and place it on top of the "-" to read 101=102-1. But that's not as sexy as the ternary solution.

Irandokhtar khanom, wasting too much time on frivolous puzzles shouldn't be rewarded, it's asocial. We need negative reinforcement, which your sweet comments are not.


IRANdokht

sooooo who won?

by IRANdokht on

Maghshoosh jan great job! not maghshoosh at all :0) 

I think Capt and Majid should come up with some really nice prizes to give away for all the time we spent on their riddles and especially for the winners. 

Sorry I missed the last few hours, I was enjoying the Happy Hour specials... 

IRANdokht


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Brains, muscles and the ternary future

by maghshoosh (not verified) on

Majid khan, If your brain hasn't developed muscular features yet, its definitely b/c you haven't realized that you can gain much more than a buzz by giving up the non-halal booze in favor of these halal concoctions:
//1pezeshk.com/archives/2007/12/post_694.html

As far as 101-102=1, all I was ranting about was that 101-10=21 holds if interpreted as base-3 or ternary numbers.

I didn't post the solution to your riddle, since I'd seen it before. But if someone can fully solve your puzzle then they should have no problem w/ this variation of it. Instead of 12 balls, start w/ 27, but this time you know a priori if the odd ball is heavier or lighter. You still get 3 weightings to find it. You can do it b/c the outcome of each weighting has 3 possibilities: 2 sides equal, left or right side heavier. So 3 weightings can distinguish 3x3x3=27 different configurations. And therein lies the common ground b/w your riddle and the triple-hijacker's: ternary representations are natural for both.

Speaking of ternary numbers, they may be ubiquitous in your future:
//en.wikipedia.org/wiki/Ternary_computer#The_...


Jaleho

maghshoosh jon, very smart!

by Jaleho on

I just came back to check if anyone got this. Your answer is awesome, however, you can move one digit and make the equation correct in base 10.

 

I'll check back tomorrow!


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Re: Capt_ahyab

by Jamshid not logged in (not verified) on

Now to solve your math riddle.

1. Assume that initially, the hotel had zero dollars in its cash register, the bellboy had zero dollar in his pocket and the three guests each had 10 one dollar bills (no less and no more) in their pockets when they get to the hotel.

2. Each guest puts ten one dollar bills on the counter. So far we have 30 one dollar bills PHYSICALLY counted for.

3. The hotel manager takes 5 one dollar bills from the register and gives it to the bellboy. The bellboy then keeps 2 one dollar bills for himself and gives 3 one dollar bills to the guests.

4. When you PHYSICALLY count all the bills, you'll get:

25 one dollar bills in the register +
2 one dollar bills in the bellboy's pocket +
3 one dollar bills in the guests' pockets =
-------------------------------------------------
30 one dollar bills PHYSICALLY accounted for. This is the same number than in the initial count.

As you can see not a single dollar bill is missing!


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capt_ahyab has 11 fingers

by Jamshid not logged in (not verified) on

Capt_Ahyab,

I have proof that you don't have 10 fingers! You have 11 fingers! Here is the irrefutable proof:

Open your hands in front of you and start counting from the leftmost finger on your left hand to the rightmost finger on your right hand.

However, don't start counting with one. Start counting with 10 and go backward, that is, 10, 9, 8, etc...

By the time you reach 6, you'll see that you are done counting your left hand fingers. So we have 6, and now add the other 5 fingers from your right hand, and you get 11.

6+5=11. Now try it on your own hands!

Remember, according to your own words, "Calculation MUST prove the same answer in both direction"!

The problem you presented is using a similar technique.

jamshid


Majid

Maghshoosh jaan

by Majid on

shoma daari ma ro ham maghshoosh mikoni ha!!

Brains are NOT considered muscles.....:-)


Majid

Wow wow wow.....HOLD ON !

by Majid on

1) forget about 1/3 this and 1/3 that......where is 3/3 answer to my riddle?

2) Yes, I'm buzzed ! it's Friday night for God's sake.....LOL

3) "Move one digit"! where did all this +....X....- ...(.....)came from? or reading from left to right or right to left ?

- OR= are not considered "digits" ! am I missing somethin?

MOVE..... not add or eliminate! right Jaleho?

And I'm NOT seeing two monitors in front of me YET! getting there though! 


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101-102=1

by maghshoosh (not verified) on

One solution would be to interpret these numbers in a base other than the customary 10. Just as a reminder, a base-2 or binary number, which would consist of only 1s & 0s, such as 1101, is read from right to left as multiples of increasing powers of 2 starting from the 0th power, so that the binary 1101 is equal to 1+0x2+1x4+1x8=13 in the customary base-10 version we use, where the digits are multiples of increasing powers of 10.

The largest digit in Jaleho's expression is 2, so it can't be a binary number, but can be a base-3 or higher number. So if we try base-3, 101 is equivalent to 1+0+1x9=10 and 102 is equivalent to 2+0+1x9=11 in the usual base-10 notation. So in that interpretation the equation is saying 10-11=1 in base-10, which is still wrong. But if you move the 2 to get 101-10=21 in base-3, then in base-10 it's equivalent to (1+0+1x9)-(0+1x3)=1+2x3.

BTW Jaleho, I didn't finish Majid's puzzle as you said. ID showed how to approach it and did 1/3 of it, I added another 1/3, and if anybody cares they can spell out the last 1/3. To be honest, I hadn't seen your puzzle before, but I'd seen Majid's some time ago and don't remember if I read or worked out the solution back then.


Jaleho

Triple hijack

by Jaleho on

move just one digit to make this equation correct:

 

101-102=1


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What's w/ the tantrum, agh Majid?

by maghshoosh (not verified) on

Your high IQ may allow you to force a face-off, but the final outcome of the confrontation will be determined by my unsurpassable BMI value of root-pi; that's right, I'm all muscle in between the ears & all the way down. Irandokhtar khanom, I'd rather you deliver the coup de grace to this hijacking ordeal.


Jaleho

Azarin, you did win!

by Jaleho on

This aghayoon pose a puzzle, but they don't know the correct answer themselves, or they just leave for the happy hour :-)

 

See, your answer was the first correct answer to Captain's, and Maghshoosh gave Agha Majid's correct answer, but agha Majid is still waiting, although given the happy hour he should see two correct answers instead of none :-) :-)


Majid

Hey hey hey......maghshoosh..........

by Majid on

Com'on now.........

Don't hijack an already hijacked blog.....OK?

I have an IQ of 265 and I hunt you down wherever you go......LOL

Mine is not solved yet!


Azarin Sadegh

Wow...

by Azarin Sadegh on

64 comments for this blog? I am speechless!

Damn! I was sure I had won the prize :(

No wonder I'm thinking of leaving the IT world...LOL!

Thanks for this fun blog Captain!

Azarin

 


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You corrected it.

by maghshoosh (not verified) on

Looks like you corrected your post and took out the reference to the fitileh "center." I just replied to that post of yours. If you didn't already know the answer & did it in a few minutes, you'd now be ready for followup puzzles, which were not any easier.


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Unclear wording.

by maghshoosh (not verified) on

Mostly the right idea, but what do you mean by "bend the other one in the center and lit both ends ,when the burn meet at the center it's another 15 minutes"? What's w/ the bending & meeting at the center? I already hinted that since the rate of burning is unknown, it won't necessarily be exactly 15 mins when the spark from 1 end reaches the exact center.


Majid

You start one "fitile" on

by Majid on

You start one "fitile" on one end, as soon as the first one is done  lit both ends of the second one ,when the burnt ends meet  it's another 15 minutes and you're out!


anonymous fish

whoo hoo

by anonymous fish on

do i win a prize? 

actually, if i just have a cold beer and a hot kiss waiting for me when i get home, i'll be a happy camper.

:-0

ps.  i gave up on the quiz.  my poor brain is frazzled enough!


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Lets go hijacked-squared

by maghshoosh (not verified) on

A friend of mine looking for a job in a mathematical field had a phone interview. W/o prior warning, the interviewer starts asking him math puzzles and expects him to answer right there on the phone. I'll drop you one of them (which some of you may have seen before), but remember that the interviewer is waiting for your answer on the phone.

You're left in a room w/ only 2 pieces of fitileh and a matchbox. All you know is that each fitileh takes 30 minutes to burn from one end to the other. You're expected to come out of the room in exactly 45 minutes, w/ no other time-measuring devices (clocks, watches, etc.) at your disposal. (But you don't have 45 minutes to solve this puzzle.)

Hints: If you realize a "trick," the solution is easy. But can't assume anything about the rate of burning of the fitilehs. E.g., can't assume that half of a fitileh will burn in 15 minutes.


Majid

OK.....for the last time before I see solution

by Majid on

This is how I want to see it presented........

On scale.....

        *  *  *

4As........4Bs...........equal..........they're gone, that's one try

Then proceed with the remaining 4 and 2 tries left

       *  *  *

4As.....4Bs.........NOT equal..........in this case 4Cs are gone, now between 4As and 4Bs,(not equal ones) which one you're going to chose to proceeds with 2 remaining tries?........and then what?

         *  *  * 

6As.........6Bs.......not equal of course.......that's one try

Which ones you're chosing to proceed with 2 tries left? heavier ones? or the lighter ones?

       *  *  *

5As.......5Bs..........equal........now you have 2 balls and 2 tries left

5as.......5Bs........not equal......other 2 are gone, which 5 you're chosing with 2 tries left?

 

 


capt_ayhab

LOL Majid

by capt_ayhab on

Here are the correct answers:

my favorite Fishie, and Ms. Mahnaz got it correct.

Booos to all, till the next riddle[Age kasi hijackesh nakoneh ha]

 

-YT


capt_ayhab

Majid

by capt_ayhab on

Actually, Mrs. and I are planning to go to OC around that time. I will take you up on your offer.

And Thanks pal for your kind words, Much obliged.

-YT


Majid

UPDATE ..... I have it !

by Majid on

OK.....what the heck! I have to come clean.......

The $1 that captain is missing........I got it! 

s**t......I didn't know one friggin Dollar can bring so many comments!

Capt.  how do I send it to you?

Can we focus on my riddle "hijacking the blog" now?


Majid

Captain kako!

by Majid on

All I can say is.......you're one cool fela.....:-)

If by any chance you're in So Cal, we all can get together for 13 be dar in Irvine and it'll a blast.

PS.  jaa ye JJ khaali