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        riddles >> easy >> Missing Shapes
        
(Message started by: Barukh on May 24^th, 2006, 1:41am)

Title: Missing Shapes
Post by Barukh on May 24^th, 2006, 1:41am

Yes, I know, such problems are often ambiguous. Still, I've found this one worth presenting.

So, here it goes (http://www.google.com/base/a/1218733/D10767345553578711408).

Source: Inspired by a problem published in weekly newspaper.

Title: Re: Missing Shapes
Post by oh_boy on May 25^th, 2006, 8:03am

Is the answer [hide]{nothing, 7 circles, 8 diamonds}[/hide] ?

Title: Re: Missing Shapes
Post by Icarus on May 25^th, 2006, 3:26pm

One pattern gives: [hide]8 triangles, 9 circles, 1 diamond[/hide]

Title: Re: Missing Shapes
Post by towr on May 26^th, 2006, 12:49am

12 circles, or 6 triangles would also work (and keeping the rest the same as Icarus' solution)

or 5 triangles 4 circles, 1 diamond

Which just goes to prove the aneristic principle (http://en.wikipedia.org/wiki/Discordianism#Philosophy) (the principle of apparant order), people can find patterns everywhere, whether they're there or not.

Title: Re: Missing Shapes
Post by JohanC on May 26^th, 2006, 3:03am

My first considerations went to
4 triangles, 9 circles and 5 diamonds
But then I wondered: why would this riddle include irrational numbers?
Maybe the rows are just added as in
4 triangles, 6 circles and 8 diamonds ?
Or 2 triangles, 6 circles and 10 diamonds to make both the rows and the columns sum to 6-12-18?

Title: Re: Missing Shapes
Post by Barukh on May 26^th, 2006, 5:11am

on 05/26/06 at 03:03:33, JohanC wrote:

But then I wondered: why would this riddle include irrational numbers?

[hide]Why not?[/hide] ;D

I would like to understand the patterns of other solutions too.

Title: Re: Missing Shapes
Post by JohanC on May 26^th, 2006, 1:45pm

on 05/26/06 at 05:11:19, Barukh wrote:

[hide]Why not?[/hide] ;D

Yes, I think it makes some sense.

Quote:

I would like to understand the patterns of other solutions too.

Oh_boy's solution also seems quite appealing considering each line as [hide]a three digit number and divide twice by two.[/hide]
Icarus seems to prefer [hide]arithmetic series for each symbol[/hide], but Towr's first guess suggests [hide]geometric series[/hide] could serve as well. Towr's other proposals are probably more clever, as I don't discover their logic.

Title: Re: Missing Shapes
Post by Grimbal on May 27^th, 2006, 9:38am

I only figured that [hide] squares + triangles = circles [/hide] but it doesn't determine all the values. I had to resort to [hide] arithmetic sequences for each shape: 1-1-1, 2-5-8 and 3-6-9[/hide] which is compatible with the sums. And in fact is what Icarus proposed.

Another solution would be 2 triangles-6 circles-4 squares:
[hide] circles = squares + triangles in rows and columns. [/hide]

Oh_boy's is the one I like most. A silly alternative to that would be [hide] 312 -> 156 -> 0, making the last row completely empty![/hide]

Title: Re: Missing Shapes
Post by towr on May 28^th, 2006, 7:08am

on 05/26/06 at 13:45:31, JohanC wrote:

Icarus seems to prefer [hide]arithmetic series for each symbol[/hide], but Towr's first guess suggests [hide]geometric series[/hide] could serve as well.

You can have one be arithmetic and one geometric as well.

Quote:

Towr's other proposals are probably more clever, as I don't discover their logic.

5,4,1 is what you get when you want to have the number of figures in each column be the same, non-zero, and minimal.

The only constant in our patterns this far is than we go with triangles, circles, diamonds for the last line.

Title: Re: Missing Shapes
Post by TenaliRaman on May 30^th, 2006, 8:38am

Icarus' answer was the first that hit me.

I have seen such questions being used in personality assessment quizzes. I wonder what one can deduce from this?