Puzzle Game

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1. What goes in the middle? (worth 50 points)
2. Explain why this goes in the middle. (worth 50 points)

I'd guess the hat shape for reasons of symmetry?

^^Yaye greetings kxmode. Thankee for this lovely game. I am very sorry if I am incorrect however I think this may be the happy little skate (shoe). I think this is due to the fact that the hat appears twice on two rows and two columns. The snow flake appears twice on two rows and once on two columns. This is reverse for the snow man. ^^ I think that I then used happy process elimination to deduce the happy skate requires to be in the middle and also this shall provide a nice crossing pattern for the skate

Hat was my first thought - a row of all hats from upper left to lower right somehow looks "right" to me.

But after thinking about it some more, my answer to what goes in the box is: whatever you want.

If we put the grid on an x/y axis such that the lower left-hand corner is 1,1 and the upper right-hand corner is 5,5, then the symmetry of the puzzle is that the cell (6-x), (6-y) will contain the same symbol as cell x, y. For example, 2,2 is a skate, and (6-2),(6-2) or 4,4 is also a skate. Likewise 2,1 is a snowman, and 4,5 is a snowman.

Based on that, the cell 3,3 is symmetrical with itself, so you can put whatever you want in there.

JSB, over-thinking things for the past 45 years.

Hat

Going from upper right to lower left the snowman and snowflake alternate and the skate and hat alternate.

(See picture below)

Last edited by MidlifeAspie on 08 Dec 2010, 5:31 pm, edited 1 time in total.

Do you play a lot of Sudoku?

it depends on which pattern you're trying to stay faithful to.

but most likely the hat.

there is no symmetry here, but if you slice the drawing from top right to bottom left the two halves are the same (if oriented the same way). this gives us no information about what the middle should be.

if you are determining the middle based on the corner-to-corner diagonals it is easily the hat, because one diagonal is all hats and the other alternates. based on all diagonals starting top left and moving toward bottom right it is likely also the hat, since on those diagonals pictures repeat (unless it's the asterisk because one has not appeared yet). based on the diagonals starting top right and moving toward bottom left, they tend to alternate so it is also the hat. based on the middle vertical and horizontal it could be anything, or the shoe.

the hat fits into the pattern in more ways than the other icons, but there really is no way of determining what is correct without asking questions.

Hat. For reasons I can't explain adequately, dammit. But hat, definitely. Not skate.

The symbols alternate along these axis lines.

Hat.

Why?

Because it completes a one pattern without disturbing another.

If the square is:

A/1 .. 2 3 4 5
B
C
D
E 5/E

That is, rows A-E and columns 1-5, then the "falling" odd-numbered diagonals (A1 to E5, A3 to C5, A5, C1 to E3, E1) alternate all hats and all skates. The missing cell is in the A1-E5 diagonal, a "hat" diagonal.

There is a second pattern, in the "rising" even diagonals, with snowflakes and snowmen in alternation, but that is irrelevant, since the missing cell is not on one of those diagonals.

There's probably a more concise rule, but those lines of hats and skates leap off the page, with the alternating snowmen/flakes only a second or two behind, and I'm a rush, so I'm going with the first thing my eyes saw.

-- RF

If you said hat award yourself 50 points! Yay!! ! Congrats you!



If your logic showed you the following pattern award yourself another 50 points! You're awesome!

I don't follow the logic of step 2. Can you clarify?

Thanks. That was fun to think about.

JSB

^^ Wooowwww, very well done everyone! Thankee very much for this lovely quiz kxmode. I am very sorry for being incorrect.

Good to see you again, Tom. Any news on your Colors scores?

Starting from the top-left, and moving in a clockwise fashion, the symbols repeat themselves with hat, snowflake, ice skate, and snowman. See it now?