Daily puzzles/problems.

Got it! (Maybe!) But it assumes that we know how much a non-counterfeit coin weighs.

1. Number the bags from 0 to 9.
2. Then, take one coin from bag number one, two coins from bag number two, three from number three, etc. (Don't take any coins from bag number zero.)
3. The total number of coins will be 45 coins.
4. ASSUMING that each non-counterfeit coin weighs some certain amount 'X', the equation "45X - WEIGHT" will yield a number of grams that matches the number of the counterfeit bag.

Scher, do we begin knowing how much a non-counterfeit coin weighs???
If not, then my plan falls apart.

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Originally Posted by billl

Got it! (Maybe!) But it assumes that we know how much a non-counterfeit coin weighs....

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That's very ingenious, even with the assumption - but it also assumes that the scales are like this. I'd assumed that they were like this, and that no marked weights were provided, so all you have to work with is the bags.

Scher?

Quote:

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Originally Posted by billl

Got it! (Maybe!) But it assumes that we know how much a non-counterfeit coin weighs.

1. Number the bags from 0 to 9.
2. Then, take one coin from bag number one, two coins from bag number two, three from number three, etc. (Don't take any coins from bag number zero.)
3. The total number of coins will be 45 coins.
4. ASSUMING that each non-counterfeit coin weighs some certain amount 'X', the equation "45X - WEIGHT" will yield a number of grams that matches the number of the counterfeit bag.

Scher, do we begin knowing how much a non-counterfeit coin weighs???
If not, then my plan falls apart.

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Yes, we do know how much each coin weigh: 10g.

(Was expecting someone to ask this question sooner :))

Bill's answer is correct:

- Put labels on the bags, numbering them from 1-9.

- Take the same number of the coins from each bag as they are indicated on their labels.

- There will be 55 coins (not 45), making the expected weight 550g; however, because of the counterfeits, total weight should be less than that and missing grams will indicate the number of the bag the coins come from.

Quote:

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Originally Posted by MarkBastable

That's very ingenious, even with the assumption - but it also assumes that the scales are like this. I'd assumed that they were like this, and that no marked weights were provided, so all you have to work with is the bags.

Scher?

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Earlier, when I answered Silas' question, I did mention that it was one of those used by jewellers.

Your turn, Bill!

HA YES!

but....

bag 1 + bag 9 +
bag 2 + bag 8 +
bag 3 + Bag 7 +
bag 4 + bag 6 +
bag 5
= 45.

Bag zero adds zero. (Imagine if Bag zero had the counterfeits...)

Wow, I feel pretty bad-***. But now I need to think of (remember) a puzzle, and that one is gonna be hard to match.

Hmm, OK, I hope that I am around enough to answer questions. Or that someone doesn't give the answer right away, if it is too obvious...

This is like the one Mark did earlier, but if you haven't heard it before, you might need to ask some questions in order to work out the answer... (Sort of like the game twenty questions... I will give only yes or no answers!)


HERE IS THE SITUATION:
A man is lying in a field, dead, next to a large rock. His body is a perfect specimen of manly health--no marks, no bruises, no visible injuries. But he is dead. What happened?

Quote:

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Originally Posted by billl

HA YES!

but....

bag 1 + bag 9 +
bag 2 + bag 8 +
bag 3 + Bag 7 +
bag 4 + bag 6 +
bag 5
= 45.

Bag zero adds zero. (Imagine if Bag zero had the counterfeits...)

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Yes, I see how this works out but in my solution you take 10 coins from bag no.10 as well, making the total 55.


Going back to your question, is the rock crucial in his death?

(btw, I can see how a 'bag 10' instead of 'bag zero' changes the math...)

Um, yes, the rock plays a role in his death.

Convinced, erroneously, of his manifest destiny, he gave himself a heart attack trying to get the sword out of the stone.

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Originally Posted by billl

Um, yes, the rock plays a role in his death.

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Since there were no visible injuries, is it safe to assume that he was not crushed by this rock?

How large is it? (And, more importantly, does size matter?)

Is it a regular rock by the way? I.e., "a large piece of stone" in the sense we use in everyday conversation?

Quote:

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Originally Posted by MarkBastable

Convinced, erroneously, of his manifest destiny, he gave himself a heart attack trying to get the sword out of the stone.

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A nice attempt, but no.

Quote:

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Originally Posted by Scheherazade

Since there were no visible injuries, is it safe to assume that he was not crushed by this rock?

How large is it? (And, more importantly, does size matter?)

Is it a regular rock by the way? I.e., "a large piece of stone" in the sense we use in everyday conversation?

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He was not crushed. Let's say that the stone was the size of a loaf of bread. It is not a "regular rock", I guess, but it is a large piece of stone, in the sense that we usually use.

Maybe he's a dreamer? Looking at the sky - his thoughts miles away - he tripped over the stone and broke his neck...

Quote:

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Originally Posted by billl

It is not a "regular rock".

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Since it is not a "regular rock", is it possible that it is something chemical/poisonous?

Is the man's age important? Or his profession?

It is a poison, I suppose, but it wouldn't kill you.

The man's age and profession are not important.

The rock is kryptonite and the man is Superman?

Yes, iamnobody guessed it!

Good one billl! Now, a riddle.

Odds are good you know my start
But do not know my end.
I sound delicious but I'm not
Be sure of that my friend.

A squiggle here, two squiggles there,
Is clearly what you see.
From here to there, how far around?
Well, it's all Greek to me.
What am I?

ouroboros?

Poorly-cooked gyros?

The greek letter 'pi'?

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Originally Posted by kasie

The greek letter 'pi'?

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Brilliant.

kasie's right. And yes, brilliant! Your turn.

Oh, dear - now I have to think of another one - sorry, folks, I'll have to sleep on this one. Watch this space. (Kasie goes off muttering and sighing to herself.)

OK - try this one.

A man of the desert lay dying - he called to his bedside his three sons and blessed them.

'To you, my eldest son, I leave one half of all my worldly goods,' he said.

'Father,' wept the young man, 'you are indeed the best of fathers.'

'To you, my second son, I leave one quarter of all my goods.'

'Dearest father, you are a loving and generous parent.'

'And to you, my youngest son, I leave one fifth of my wealth.'

'Father, I thank you,' cried the youngest son though his voice was muffled by tears and he could hardly be heard.

'There is one condition,' the old man murmured with difficulty, for his end was drawing near. 'It has taken me many years to acquire my flocks and herds. Do not, I pray you, kill any of the beasts as you divide them among yourselves.'

'Father,' the young men promised, 'it shall be even as you request.'

'Should you have difficulty over the division, send for your uncle,' whispered the old man. 'He will surely come to your aid.'

And so saying, the worthy old man passed to a better world.

The three sons performed the funeral rites with all due ceremony, amid much mourning, for they were dutiful sons and had loved their father. When it was fit and proper so to do, they began the division of their inheritance, according to their father's wishes. The flocks of sheep divided easily, as did the herds of goats. But when it came to allotting the camels, they found themselves much exercised, for there were nineteen camels to be shared.

'How shall we do this?' they asked themselves, 'for surely we cannot divide nineteen camels in the way our good father directed unless we kill one and that he specifically forbade.'

Then they remembered their father's advice and sent for their uncle. It took some time for the old man to arrive, for he lived many miles away across the desert. The three young men knew how to greet an honoured guest and welcomed him, leading him to their tent to rest and refresh himself. They gave orders that his tired camel should be fed and watered with their own animals.

After their meal together, the young men begged their uncle to help them solve their dilemma.

'Ah,' said the old man with a smile, 'my worthy brother's fine camels! I always admired them. Allow me, I pray, to look on them again.'

The young men took him to the place where the camels were tethered. He smiled broadly when he saw how healthy and well-cared for they were.

'My dear nephews,' he cried, 'I see no problem. The answer is before you.'

So - what is the answer? How can the camels be divided according to the old father's will?

They could imagine that the uncle's camel actually belonged to their father. Or, perhaps, the uncle could just lend it to them. That would make twenty camels, and thus the brothers could receive their alloted numbers:
1/2=50%=10 camels
1/4=25%=5 camels
1/5=20%=4 camels

There would still one camel (5%) remaining amongst the 20, and since the uncle had merely lent it, he could just have it right back.

Quote:

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Originally Posted by billl

They could imagine that the uncle's camel actually belonged to their father. Or, perhaps, the uncle could just lend it to them. That would make twenty camels, and thus the brothers could receive their alloted numbers:
1/2=50%=10 camels
1/4=25%=5 camels
1/5=20%=4 camels

There would still one camel (5%) remaining amongst the 20, and since the uncle had merely lent it, he could just have it right back.

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Nice!

That's right, billl - over to you.

OK, I'm gonna try and come up with something. Maybe I'll have to check out a puzzle website or something, because I can't remember any...

In the meantime, please, if anyone else has a good one, go right ahead and post it!

(EDIT: I will be back online and will at the very least cut and paste something from a website probably between 7 and 12 hours from now, if no one else has a good one...)

Which wartime U.S. president is famous for:

1) side-burns
2) top hat
3) blonde hair
4) not finishing his term

OK, I am gonna just give the answer to that latest puzzle that I made up by myself. The answer is:

Abe Lincoln

HERE IS THE NEXT PUZZLE!

This is copy and pasted from Wikipedia

Quote:

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Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself.

Now that each of the guests has been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2. If the guests originally handed over $30, what happened to the remaining $1?

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I'm sorry, I feel cheap for doing this.... But I wanted to give you guys an interesting, PROFESSIONAL, brain-teaser...

You don't need to add the 2 and 27 because the 2 is already included within the 27...I think.

Yep--for the guests, that $2 that the bellhop is holding is an overpayment on their part, and it is included in the $27. Good work--people can check the Wikipedia link up there for the fleshed-out answer...

...but it is just a trick going on when it is suggested that the $2 be added to the $27 for some reason. The $2 is actually just what is left over from the $5, after the customers got their $3. If the bellhop, in a fit of honesty, went back and gave the $2 to one of the guests (or divied it up somehow, e.g. $o.66 each), then we would see that the guests had no longer overpaid the two dollars. Their $27 total payment would finally be reduced to the $25 that they actually owed.

Here's a quick easy one while we're waiting for billl

8 9 6 3 2 1 4 ?

I have to do another (non-researched) one? I will keep trying, because this is a great thread, but I am having trouble remembering another one. I like the more social/conversational mood here, where we are posting from our memory of these puzzles, but I might have reached my limit. But I will keep trying, because I probably will come up with something eventually :)

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Originally Posted by prendrelemick

Here's a quick easy one while we're waiting for billl

8 9 6 3 2 1 4 ?

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I find this one neither quick nor easy.

7!

Re-arranging the sequence as consecutive top-to-bottom columns, we get:
8 2
9 1
6 4
3 ?
Paired thusly, it seems that adding 7 to 3 will give us 10, just as the other pairs do. Nice one, did you make that one up yourself?

Assuming that I am correct (and there might very well be some other solution you had in mind...), I will next post a classic 'puzzle' that I finally managed to remember.

Game Show Problem

You have been called down from the audience to participate on a game show. The host stands with you before three large curtains, numbered 1, 2, and 3. Behind one of the curtains, there is a check for $10,000. The other two curtains have nothing behind them. You must decide which curtain you think conceals the prize.

After you have chosen (for example, curtain number 1), the host gives you one more chance to change your mind. But before you decide whether or not to change, the host will pull aside one of the curtains that you have not chosen (for example, curtain number 2), in order to show that there is nothing behind it.

So, what should you do:

1) choose the other curtain (in the example, curtain number 3)
or
2) keep to your original choice (e.g. curtain number 1)

and Why?


(I hope I explained this one well, please ask if anything needs clarification...)

I know you have to change, but I always thought it went against all common sense :nod: No matter how good the explination :lol: It's a bit like the hare and the turtle...

The first time you have a 1 in 3 chance to get it right. The second time, when you choose the other curtain, you have a 1 in 2 chance. BUT that goes for both doors, so that wasn't the explination
Erm...
The chance you have it right the first time, is 1/3. So you probably have it wrong (2/3). After the curtain with nothing behind it is opened, you better switch to the one that is left (neither chosen the first time or openend). But what the chances are for that one, I'm not sure. I just know they're better :crazy:

If anybody knows how to explain this more clearly, please do!

Quote:

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Originally Posted by billl

7!

Re-arranging the sequence as consecutive top-to-bottom columns, we get:
8 2
9 1
6 4
3 ?
Paired thusly, it seems that adding 7 to 3 will give us 10, just as the other pairs do. Nice one, did you make that one up yourself?

Assuming that I am correct (and there might very well be some other solution you had in mind...), I will next post a classic 'puzzle' that I finally managed to remember.

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I just went clockwise round the number pad on my keyboard:D but 7 is right.

This is a maddening one, actually - because the odds are completely dependent on when you assess them.

You could say that once you're down to two curtains, it's fifty-fifty which is the prize curtain, so why change.

But actually, that's not quite true - and it's because you've been made to choose before you get to that point.

Imagine there are a million curtains. You choose one. They take away all but one of the others.

At that point it's pretty obvious that the chances of you having picked the right one are one-in a-million. And pretty obviously, you'd swap, because they know which is the right one, so you'd tend to believe that they've got it right because you got it wrong.

The same principle applies with three curtains, but the odds are shorter. The fact remains, however, that it's absolutely certain they've picked the right one of two if you haven't already picked it, but only one in three that you picked the right one in the first place.