Question of the Day #319 (11/8/10)

[Kazza]

I am doing some renovating. I have some fancy floor tiles, enough to provide a border in 2 rooms. I'm not sure how to arrange them. If I set a border of 2 tiles all around, there will be 1 left over; if I have 3 tiles all around, or 4, or 5, or 6, there's still 1 tile left over. I then try a block of 7 tiles for each corner, and I come out even. What is the smallest number of tiles I used to get this result?


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[sxty8goats]

Either I'm missing something in the question or the question isn't worded correctly.

The first line indicates that the number is odd.

The last line actually gives you a solid number, which is even. 7x7 block in each corner of 2 rooms is 7x7x8.

 

[Kazza]

Either I'm missing something in the question or the question isn't worded correctly.

The first line indicates that the number is odd.

The last line actually gives you a solid number, which is even. 7x7 block in each corner of 2 rooms is 7x7x8.

I hear ya, but this question is on several different quiz pages and I've only changed a few words - none of which would make a difference to the question.

Maybe when the answer is posted it will all make sense

 

[FizzySix]

You need a tile cutter? :thumbup:

 

[rsw81]

No offense Kazza, but this is a mathemathical impossibility unless there is some play on words you are trying to get away with. I was dumb enough to actually write out all the different sets of simulatneous equations with variables designated to each side of the two rooms and the equations become inequations when attempting to solve for any given variable.

I'm curious to see what you found as the answer.

 

[Kazza]

I'll post the answer up when I'm home this evening - see if it makes sense then, if not EPIC FAIL...... LOL

 

[JustinID]

I spent about 30 minutes racking my brain on this one earlier today... had to stop and study for a final exam. I also can't make heads or tails of it. I tried "thinking outside the box" on some of the wording and just can't come up with a real set of math problems that make sense.

sxty8goats - I don't think that the problem means a 7x7 pattern, but rather a corner pattern that utilizes 7 tiles. Of course, that's probably wrong too. haha

Looking forward to the answer on this one.

 

[Kazza]

I am doing some renovating. I have some fancy floor tiles, enough to provide a border in 2 rooms. I'm not sure how to arrange them. If I set a border of 2 tiles all around, there will be 1 left over; if I have 3 tiles all around, or 4, or 5, or 6, there's still 1 tile left over. I then try a block of 7 tiles for each corner, and I come out even. What is the smallest number of tiles I used to get this result?

There are 301 tiles. This is the smallest number that will give you a remainder of 1 when divided by 2, 3, 4, 5, and 6, but divided by 7 leaves no remainder.


NO WINNERS.

Does this make sense to you guys or is this AN EPIC FAIL?......

Let me know

 

[sxty8goats]

I spent about 30 minutes racking my brain on this one earlier today... had to stop and study for a final exam. I also can't make heads or tails of it. I tried "thinking outside the box" on some of the wording and just can't come up with a real set of math problems that make sense.

sxty8goats - I don't think that the problem means a 7x7 pattern, but rather a corner pattern that utilizes 7 tiles. Of course, that's probably wrong too. haha

Looking forward to the answer on this one.

Either way, you still have 8 corners. So the number of tiles used would still be an even number, unless you had a short wall somewhere. I suppose you could assume a short wall but the way I read the question it seemed that the 7 tile block was a 7x7 block in each corner instead of a border. Oh well.

There are 301 tiles. This is the smallest number that will give you a remainder of 1 when divided by 2, 3, 4, 5, and 6, but divided by 7 leaves no remainder.


NO WINNERS.

Does this make sense to you guys or is this AN EPIC FAIL?......

Let me know

I suppose that you could have a short wall in one of the rooms.

 

[sxty8goats]

One of the things about this question that really threw me was the changing boarder depth. If you have a fixed number of tiles and using a 2 tile deep border leaves one tile extra, then you try again with 3 deep border and you end up with 1 extra, your room shrank. That is why I assumed the 7 tile block was did not include a boarder and was 7 x 7.

 

[SirIsaac]

There are 301 tiles. This is the smallest number that will give you a remainder of 1 when divided by 2, 3, 4, 5, and 6, but divided by 7 leaves no remainder.


NO WINNERS.

Does this make sense to you guys or is this AN EPIC FAIL?......

Let me know

Still makes no sense to me for the same reasons as sxty8goats. How was the problem originally worded before you edited to make it google-proof?

 

[JustinID]

The answer is sensible on its own (solid, accurate math). It doesn't seem to answer the question though... Or rather, the question doesn't ask the right thing.

 

[rsw81]

The answer is sensible on its own (solid, accurate math). It doesn't seem to answer the question though... Or rather, the question doesn't ask the right thing.

This is exactly right. The math is correct in that 301 leaves a remainder of one when divided by 2, 3, 4, 5, or 6, but divides by 7 evenly. However, the question does not ask this in the stem of the word problem.

I normally love the math QOD's, and was a math teacher for several years. This problem makes no sense, even now knowing the answer. Sorry Kazza. Keep 'em coming though! Love the QOD's.

 

[Kazza]

Here is the original question, before I google-proofed it


You have a huge box of beautiful decorated tiles, enough to provide a border in two rooms. You really can't figure out how to arrange them, however. If you set a border of two tiles all around, there's one left over; if you set three tiles all around, or four, or five, or six, there's still one tile left over. Finally; you try a block of seven tiles for each corner, and you come out even. What is the smallest number of tiles you could have to get this result?

There are 301 tiles. This is the smallest number that will give you a remainder of 1 when divided by 2, 3, 4, 5, and 6, but divided by 7 leaves no remainder.

 

[JustinID]

If it makes you feel any better, the issue is definitely with the original question, not with any of the changes you made.

As rsw81 said, I also love the math QoDs (and they're all amusing to read/try) so keep 'em coming.