Y not we start working out some good puzzles..

You have two hourglasses: a 7 minute one and an 11 minute one. Using just
these hourglasses, accurately time 15 minutes.

You start both ( 7 and 11) running. When 7 is empty you start meassuring time (you have 4 min left in 11) when 11 is empty you turn it around then when it is empty you have 4 + 11= 15 min.

*claps* good work, i never would have thought of that

You come to a fork in the road and encounter a native standing in each fork. One always lies and the other always tells the truth. If you follow one, he will lead you to a friendly village and a great feast. If you follow the other, he will lead you to a village of canibals and you will be the feast.

You can only ask two questions. What two questions would you ask and how would you address them?

#1) Ask the native, "Are you alive?" - Obviously the answer would have to be yes, so you could easily determine which is the liar and which of them is not by their answer.

#2) After you identify which one tells the truth, simply ask him "Do you belong to the village of cannibals?", and follow whichever of the natives accordingly.

I think the better version is you have only one question. Tougher. Let you work it out :)

Lava

Very good, Lteran.

How can you tell if the following number is divisible by three using only pencil and paper and NOT using ANY math? Not interested in 'yes' or 'no', just the method of solution.

83645986503826489327453049058437463748759439438740

Please #define math.

NO math of any kind! You can count, but not add, subtract, multiply or divide. Use the paper and pencil to write the number down if you must. Like I said, I'm not looking for a 'yes' or 'no', just the method to be used. It can actually be done in seconds, and is taught in some schools.

BTW, the number cannot be divided by three.

Yours is easy marv, but impossible for those that dont know.

The one question only version, really the proper version of the original q is both tough and solvable for those that dont knwo it.

Lava

So what is the solution, Lava?

Then I've got another puzzle.

OK.

A number is divisible by 3 if you add all its numbers up and it comes to 3, 6, 9, 12, 15, 18 etc. So you can repeat the trick for huge numbers.

The one question only solution to the fork in the road is to ask one of them 'which way would the other person say leads to the cannibals'. Which ever one you ask, they'll tell you the wrong way: follow where they point to avoid being eaten.

Lava

That's because the liar always lies and the truthful one also, in this case, since he's speaking for the other guy ...

Here's another one:

Three friends check into a hotel for the night. The clerk tells them the bill is £30, payable in advance.
They each pay the clerk £10 and go to their room.
A few minutes later, the clerk realizes he has made an error and overcharged the men by £5.
He asks the porter to return £5 to the friends.
The porter sees this as an opportunity to make £2 as he reasons that the three friends would have a tough time dividing £5 evenly among them; so he decides to tell them that the clerk made a mistake of only £3, giving a pound back to each of the friends.
He pockets the leftover £2.
Now, that each of the three has got a pound back, they each have paid £9 for the room which is a total of £27 for the night.
We know the porter pocketed £2 and adding that to the £27, you get £29, not £30 which was originally spent.

Where did the other pound go?

i did a visual with it, and i cant see any money dissappear, the numbers are confusing

83645986503826489327453049058437463748759439438740

Working left to right:

Eliminate zeros and single digits with a factor of three...
8..45.8.5..82.48..2745..4..584.74..74875.4..4.874.

Eliminate single digits that appear three or more times in groups of three (this is a shortcut to get rid of digits)...
............2.....2........5..........75......874.

Eliminate remaining adjacent paired digits with a factor of three...
............2.....2....................5........4.

And again (repeat as necessary)...
............2.....2...............................

When what remains does not have a factor of three, the answer becomes no.

You could use addition, as Lava did, by eliminating any number of single digits which add up to a sum having a factor of three. That would also be faster than going the "adjacent paired digit" route.

83645986503826489327453049058437463748759439438740
8..45.8.5..82.48..2745..4..584.74..74875.4..4.874.
................................................4.

I'm gonna get flack over whether math was used (factors), but when I was taught math in elementary school in the forties, we had to MEMORIZE the multiplication tables up to a product of 100. I don't have to mentally divide 57 by 3 to recognize that it has a factor of 3, so I don't consider that "using" math. There was no "New Math" for us then.

Three friends check into a hotel for the night. The clerk tells them the bill is £30, payable in advance.
They each pay the clerk £10 and go to their room.
A few minutes later, the clerk realizes he has made an error and overcharged the men by £5.
He asks the porter to return £5 to the friends.
The porter sees this as an opportunity to make £2 as he reasons that the three friends would have a tough time dividing £5 evenly among them; so he decides to tell them that the clerk made a mistake of only £3, giving a pound back to each of the friends.
He pockets the leftover £2.
Now, that each of the three has got a pound back, they each have paid £9 for the room which is a total of £27 for the night.
We know the porter pocketed £2 and adding that to the £27, you get £29, not £30 which was originally spent.

Where did the other pound go?£30 cost less £5 refunded = £25. £25 + £3 (returned) + £2 (kept by porter) = £30. The £1 disappeared in the clever wording of the puzzle. The £2 should be added to £28, the corrected cost of £25 plus the £3 returned by the porter, and not the £27.

NO math of any kind! You can count, but not add, subtract, multiply or divide. Use the paper and pencil to write the number down if you must. Like I said, I'm not looking for a 'yes' or 'no', just the method to be used. It can actually be done in seconds, and is taught in some schools.

BTW, the number cannot be divided by three.

But cannot add? Yet you can count? Which pretty much equals adding?

-.-

You could use addition, as Lava did, by eliminating any number of single digits which add up to a sum having a factor of three. That would also be faster than going the "adjacent paired digit" route.

And Lava's way was correct?

OK.

A number is divisible by 3 if you add all its numbers up and it comes to 3, 6, 9, 12, 15, 18 etc. So you can repeat the trick for huge numbers.

Doubleplusunwrong...?

Like I said, please define the condition 'math' before asking us to not use math, because now I'm very confused. To be honest, everything in the end really can be counted as "math". Thanks. :bugeye:

More factor puzzles using "quick math": How do you determine if four is a factor of a number? How do you determine if six is a factor of a number? How do you determine if eight is a factor of a number? How do you determine if nine is a factor of a number?They're all roughly similar to the "3 factor" puzzle.

lil'miss, I didn't use math, I used a skill I learned in school long before pocket calculators were invented. Lava simply demonstrated an alternate method of solution which is faster. It's all called "quick math", but don't let the terms confuse you.

Now please define "Doubleplusunwrong". :D

Call me demie :) lil'miss sounds like I'm one of those 20-year-old aristocratic bloat-offs.

Read 1984, by Geoge Orwell @doubleplusunwrong. No spoonfeeding xP! You will see quickly here that I love doublespeak as a weapon of sarcasm.

I'm not confused at the terms, I'm confused at the fact that you expect us to solve a riddle following your guidelines without explaining them first. Now I understand. Thank you =)

The £1 disappeared in the clever wording of the puzzle.


Correct. Keep your eye on the ball, and don't get distracted. Same happens in debates a lot but people don't notice something wrong with it as easily.

"Watch the knife, not the eyes"

free after Duncan Idaho

You're welcome, demie. Mmmmmmmmm, "bloat-off", you must be Brit.

mercurio, I'll confess that I'd come across that puzzle some years ago. I'd forgotten the solution except that the 2 had to be added to the 28 and not the 27. But I still had to figure out why. That puzzle is always a good one and will get you either a beer or a punch in the nose in a bar! :D

Here's another: which is heavier, a pound of feathers or a pound of gold? Yes, one weighs more!

It's also a good bar bet - if you carry a dictionary to prove the answer.

Hahahahahaha, what a far cry. I'm Chinese. I assume you were being sardonic. Btw, I am getting spammy so I'll stop.

My bad! "Bloat-off" just sounded British. Now back to the puzzles.........

'Weigh' can mean a lot of things.

[sorry for the late edit]

Riddle:

I turn around once.

What is out will not get in.

I turn around again.

What is in will not get out.

what am I?

A klein bottle?

'Weigh' can mean a lot of things.Not in this case. It's very straight forward. Consider the feathers and gold on a balance scale. That's why I gave the clue of 'dictionary'. BTW, the dictionary is also useful in warding off the sore loser in the bar. :D

Riddle:

I turn around once.

What is out will not get in.

I turn around again.

What is in will not get out.

what am I?A turnstile?

a revolving door?

nither the mass is the same. the difference is in volume not mass. Oh and by the weigh the weight is the mass * 10 (9.8 if you want to be more accurate) so its still the same its just now in N insted of pounds or Kgs

this is an easy one

what goes on 4 legs in the morning, 2 legs in the day and 3 legs in the everning?

the riddle of the spinks (sorry its the only one i could think of off the top of my head)

nither the mass is the same. the difference is in volume not mass. Oh and by the weigh the weight is the mass * 10 (9.8 if you want to be more accurate) so its still the same its just now in N insted of pounds or KgsWrong. Try again. The mass IS different and volume has nothing to do with it.

what goes on 4 legs in the morning, 2 legs in the day and 3 legs in the everning?Man. Morning = infancy, day = adulthood, evening = old age (with a cane). Yeah, it's kinda old, but surprisingly a lot of people don't get it.

Puzzles and riddles are cool. There ought to be a separate forum just for them.

Nobody giving a try at the 4, 6, 8, and 9 factor "quick math" solutions? There ought to be some math wizards that have come across them somewhere.

um is pound a measure of volume or mass?

because if i take a kg of ANYTHING and a kg of anything else i still have equal mass and different density maybe. water and oil have different densitys but if i have a Kg of both i still have 2 kgs no matter what

marv people either know them or dont, working those out from scratch is just too difficult.

Lava

Pound is the main english currency. A pound of feathers would weigh more.

Lava

Okay. Precious metals like gold are measured in troy weight, or 12oz. to the pound. Feathers would be weighed in avoirdupois, or 16oz. to the pound. But an ounce is an ounce whichever system you use; it's just whether you have 12oz. or 16oz. to the pound. :D

Forget the metric system because I posed the puzzle in POUNDS. But you're right Lava, I shouldn't be culturally specific.

I give up. Tomorrow I'll post the solutions to the 4, 6, 8, and 9 factor problems. Mmmmmmmmm, they're so simple. It's just that pocket calculators have displaced the need for that knowledge.

Riddle:

I turn around once.

What is out will not get in.

I turn around again.

What is in will not get out.

what am I?

Hourglass?

A klein bottle?

Duh. Kudos for cutest answer! But no, it's not a Hausdorfed Banana, either.

:D

A key.

Riddle:

I turn around once.

What is out will not get in.

I turn around again.

What is in will not get out.

what am I?

You said a key, but I dont think that works.

"I turn around once.
What is out will not get in."
implies that it is now locked.

"I turn around again."
this could only unlock it.

"What is in will not get out."
incorrect, it must now be unlocked.


A workable answer would be a pump.

Lava

DAMIT your right

its a heart

Here goes: If a number ends in '00' or two digits that have a factor of four, thenumber has a factor of four, Six is a factor of any even number having a factor of three, If the final three digits have a factor of eight, the number has a factor of eight, Nine is a factor of any number if the sum of the digits has a factor of nine.That's "quick math" factoring.

mercurio, do you mean Hausdorff?

Awww, they're both Felixes. Isn't that just darling? :bugeye:

Yep, soory vor da tybo.

Your remark reminded me of one of the most daring titles for a math paper EVER:
couldn't find the exact title but it went like :"Yes, we Hausdorff bananas today.."

Serious paper, mind you. Guy was into crazy topologies like Klein en Kolgomorov.

Although as fractals come, I like my homebrew crazy Lyapunovs best... ;)