3.

In base

*x*, a number is 10101. The same number is 273 in base

*x+6*

What is x? (ie, the base of the first number)

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-) |

Guest Message by DevFuse

Started by unreality, Mar 03 2008 04:08 AM

26 replies to this topic

Posted 03 March 2008 - 11:01 PM

Here's another riddle, I just thought this one up:

3.

In base*x*, a number is 10101. The same number is 273 in base *x+6*

What is x? (ie, the base of the first number)

3.

In base

What is x? (ie, the base of the first number)

Posted 03 March 2008 - 11:03 PM

Statman, your #2 answer is correct, though for #1 you might be surprised to know there are only two answers (or 4 if you're picky). Look at my spoiler in the post above yours on the first page your answer is correct, but you only went halfway

Posted 03 March 2008 - 11:06 PM

EventHorizon, 0x0 wouldnt be a rectangle ;D it would be a single point. Like how 1x0 rectangle is actually a line.

A 0x3x3 rectangular prism isnt actually a 3d rectangular prism as one of its dimensions is 0- it's a 2-dimensional object, as geometry goes. If a dimension is 0 then it's not counted as a dimension in geometry- it has to have some value to extend the axis in that direction. We don't say that a square has 5 dimensions if its 0x0x0x2x2, know what i mean?

yes, but I was simply finding the values could be substituted for the width and length to fulfill the "number of shaded squares equals the number of squares in the center." 0X0 can be argued not to be a rectangle, but it is still a degenerate case of a rectangle. So I guess I should have said "degenerate case" instead of "trivial answer." I still believe it could/should be included.

Posted 03 March 2008 - 11:14 PM

Here's another riddle, I just thought this one up:

3.

In basex, a number is 10101. The same number is 273 in basex+6

What is x? (ie, the base of the first number)

Spoiler for answer

edited to remove any confusion with bases

**Edited by EventHorizon, 03 March 2008 - 11:17 PM.**

Posted 04 March 2008 - 02:08 AM

yes, but I was simply finding the values could be substituted for the width and length to fulfill the "number of shaded squares equals the number of squares in the center." 0X0 can be argued not to be a rectangle, but it is still a degenerate case of a rectangle. So I guess I should have said "degenerate case" instead of "trivial answer." I still believe it could/should be included.

Too bad my edit time expired...so here's a new post. Any degenerate case of a rectangle (either dimension is 0) will work.

So....how about in 3 dimensions....where each border cube is "shaded"?

Posted 04 March 2008 - 10:04 PM

You got #3 right ;D

as for the 3d rectangular prism with border cubes shaded:

2x+2y+2z-8 = number of shaded cubes

2x+2y+2z-8 = xyz/2

*2

4x+4y+4z-16 = xyz

+16-xyz

4x+4y+4z-xyz = 16

*-1

xyz-4x-4y-4z = -16

hmm. Not sure how to make that factorable lol. There's *probably* a way, I'll think on it

as for the 3d rectangular prism with border cubes shaded:

2x+2y+2z-8 = number of shaded cubes

2x+2y+2z-8 = xyz/2

*2

4x+4y+4z-16 = xyz

+16-xyz

4x+4y+4z-xyz = 16

*-1

xyz-4x-4y-4z = -16

hmm. Not sure how to make that factorable lol. There's *probably* a way, I'll think on it

Posted 04 March 2008 - 11:03 PM

Why can we not use rectangles with a width of 1? there is an infinite amount of answers this way .. (1x2,1x3....1x4761) did i miss something?

Posted 04 March 2008 - 11:09 PM

Why can we not use rectangles with a width of 1? there is an infinite amount of answers this way .. (1x2,1x3....1x4761) did i miss something?

Lets say the rectangle is 1Xx. Then there are x total squares, and all of which are shaded (all on the border). There are no unshaded squares. Therefore the number of shaded squares are not equal to the number of unshaded squares.

So rectangles of this sort will not work.

Posted 04 March 2008 - 11:13 PM

hi, im new. allow me to ask the dumb questions for a whileLets say the rectangle is 1Xx. Then there are x total squares, and all of which are shaded (all on the border). There are no unshaded squares. Therefore the number of shaded squares are not equal to the number of unshaded squares.

So rectangles of this sort will not work.

Posted 04 March 2008 - 11:20 PM

hi, im new. allow me to ask the dumb questions for a while

Certainly. I'm fairly new to this site too, but like to explain things to people.

There are no dumb questions so long as you learn from them.

0 members, 0 guests, 0 anonymous users