Brainteasers and Other Puzzling Recreations

[SDJs]

I've searched the threads and can't find one of this sort, so I'll start one. If there is one already, I apologise and I'll crawl back into my hole.

As indicated by our collective affection towards what is generally considered to be a more time-consuming, although better shave, I have concluded that most of the members here, myself included, enjoy spending time simply taking time over things and mulling things over. I do this in various ways, one of which is to (try to) solve puzzles.

I'm not a mathematician, nor am I a member of MENSA, which is why it probably takes me a reasonable amount of time to solve most brainteasers. I suppose that's why it becomes a rather rewarding task. So I started this thread to appeal to those who enjoy puzzles just as much as I do. I'll post the first one in just a moment. Hopefully this might persuade others to contribute. Please do.

Might I suggest that if you know the answer, you don't just post it normally, as this would spoil it for others who may still be toiling over the answer, but to hide it as so

Spoiler

This is an example of spoilerized text.

Also, I would urge you to not just copy and paste the question into google to find it and what would be the answer that probably lies an easy stone's throw away.

Well, here goes...........

I keep one spare tyre in my car. Last year, I drove 10,000 miles in my car, and rotated the tyres at intervals so that, by the end of the year, each of the five tyres had been used for the same number of miles. For how many miles was each tyre used?

 

[ouch]

Spoiler

That one was too easy.

 

[Mike H]

Spoiler

Ouch is is president of the MENSA Overlords Society, easy for him. I thought it a nice puzzle.

Spoiler

8000 miles each

 

[59chop]

I have no idea how to build a 'spoiler' but this solution will seem too straightforward to be right... I think its _____

Did I get it???

 

[SDJs]

I have no idea how to build a 'spoiler' but this solution will seem too straightforward to be right... I think its _____

Did I get it???

Not too sure about that. Ouch says too easy, but curiously no answer. Okay, here's another, still keeping it moderately simple

You have 2 hourglasses; a 4-minute hourglass and a 7-minute hourglass. You want to measure 9 minutes. How can it be done?

 

[ras120]

Okay, I was way off on this one and have changed my answer.

Spoiler

8000 per tire

 

[ras120]

You have 2 hourglasses; a 4-minute hourglass and a 7-minute hourglass. You want to measure 9 minutes. How can it be done?

Spoiler

Fill the 4 minute hourglass and pour the sand into the 7 minute hourglass. Then refill the 4 minute hourglass and again pour the sand into the 7 minute hourglass. Dump the sand out of the 7 minute hourglass and pour the sand that is left in the 4 minute hourglass into the 7 minute hourglass to make 1 minute of sand in the 7 minute hourglass. Refill the 4 minute hourglass and pour that sand into the 7 minute hourglass to make 5 minutes of sand in the 7 minute hourglass. Refill the four minute hourglass for 9 total minutes.

 

[Duckster]

Tires

Spoiler

Rotate every 2000 miles = 8000 miles on each tire

Hourglasses

Spoiler

Tip the 4 minute hourglasses on it's side (jiggle or roll it so sand is equal in both ends of the hourglass). Then run the 7 minute hourglass as normal. When the 7 hour glass has run down all it's sand, tip the 4 hour glass on end to run it's 2 minutes of sand. 9 minutes total.

 

[59chop]

How the heck do I build a 'Spolier' window?

 

[luvmysuper]

How the heck do I build a 'Spolier' window?

use a left bracket [ then the word spoiler then a right bracket ]
Type your answer after that.
After your answer type left bracket [ forward slash / then type spoiler and then a right bracket ]

So it looks like this -

[spoiler]My Answer[/spoiler]

 

[DonN]

luvmysuper , where within B&B is that explained , in ShaveWiki ????

 

[luvmysuper]

At the bottom right of the page is a section called "Posting Permissions". In that box is a blue "BB Code is on".
If you click that, it takes you here;

http://badgerandblade.com/vb/misc.php?do=bbcode

 

[AABCDS]

...
Okay, here's another, still keeping it moderately simple

You have 2 hourglasses; a 4-minute hourglass and a 7-minute hourglass. You want to measure 9 minutes. How can it be done?

I figured out how to measure eight minutes but couldn't figure out how to get to nine. I read the answer online; I was simply missing the last step.

 

[ras120]

Well, this certainly turned into a highly entertaining thread.

 

[Hineas]

Here's my answer for the hour-glass one and a rebuttal against the prior answers

Spoiler

First off, I have never had an hour glass you can open up and fill with sand (although I know you can get one), but let's make the assumption you can't fill and re-fill the sand...

Second, have you ever tried getting exactly the same amount of sand in both sides of an hour glass? Not an easy task--but it could work with some effort. Here is an alternate solution.

Step 1: Start BOTH hour glasses and let them run.
Step 2: When the 4 minute glass finishes, turn it over. Result is 3 minutes left in 7 minute glass. Total time to this point: 4 minutes
Step 3: When the 7 minute glass ends, turn it over. Result is 1 minute of sand left in 4 minute glass. Total time: 7 minutes.
Step 4: Let the 4 minute glass end. No need to turn it over. Result is that 1 minute of sand has fallen out of the 7 minute glass--so 6 minutes of sand on top and 1 minute sand on bottom. Turn over the 7 minute glass now. Total time: 8 minutes.
Step 5: wait for the 1 minute of sand fall in. Total time: 9 minutes.

 

[Hineas]

This is a great post! I might actually subscribe to this one...

 

[SDJs]

Hineas's answer for the hourglasses is spot on. Thanks ....it saves me posting the answer. Most others have posted the correct answer for the tyres problem.
Next up is a teaser which is very appropriate for this forum.

Due to rumours that there is a world shortage, people have been hoarding packs of razor blades. By the time I got to the supermarket, there were no packs left. However, the two people before me had bought 3 packs and 5 packs respectively, and they offered to share them with me so that we each took home the same number of blades. I paid them $8.

How did they divide the $8?

(I anticipate a little disagreement.....ahem.....I mean discussion, over this one due to factors which are not entirely mathematically related, ...but we'll see. Also, if anyone has a puzzle to submit, please do. I'm ready and waiting. But not THAT ready.)

 

[ouch]

Just quickly doing it in my head, I'd give the guy who had 3 packs $1 and the guys who had 5 packs $7.

My wife would argue with them until they each gave her $20 to go away.

 

[Vickers]

Spoiler

What kind of blades?

 

[Hineas]

My answer on the blades:

Spoiler

I agree with the above answer. $7 to the first guy, $1 to the second. Here is why:
8 blades divided between 3 people is 2 2/3 packs per person
If I pay 8 dollars for the 2 2/3 packs, that comes out to $3 per pack (8 blades divided by 2 2/3 packs)
The first guy gives me 2 1/3 packs (5 - 2 2/3) and the second guy gives me 1/3 packs (3 - 2 2/3)
So I pay the first guy $7 ($3 per pack * 2 1/3 packs) and the second guy $1 ($3 * 1/3 pack)