[bonanova]

The Mensa Town Council has just created the world's largest digital display in the town square.

Thirty-six digits were placed -- logically, of course -- in a huge 6x6 grid.

Last night *gasp* four of the digits were stolen.

6 4 7 8 3 7

8 2 5 1 5 6

3 - 8 6 4 8

8 6 5 3 7 6

5 4 7 - - 5

- 8 6 4 7 8

The owner of the display found your Digital Supply ad in the yellow pages and called for your help.

You arrive; and, after a moment's thought, you pull four digits from your bag and begin the restoration project.

Which four digits did you select?

Where did you place them?

Why?

[Izzy]

We're missing 2,7,7,8. As for where they go... Give me a minute.

[Gambit]

Ok i get it now.

1 one, 2 two's, 3 three's,...

so this is missing 2,7,7 and 8.

still not sure where they go though

<_<

[Izzy]

I still don't know where they go. I taking one number at a time, and adding up the numbers around it. 38 was common, but there were some 45s and stuff.

I'm somewhat sure the two goes at (2,4).

[Guest]

6 4 7 8 3 7

8 2 5 1 5 6

3 -7- 8 6 4 8

8 6 5 3 7 6

5 4 7 -8- -2- 5

-7- 8 6 4 7 8

The posts above explained how we got to the numbers. I placed them where I did based on this logic: I didn't see any duplicate digits either horizontally, vertically, or diagonally. This is the only sequence that continues that pattern.

[Izzy]

Hmm, well it makes sense, but my gut tells me it isn't right. The words Mensa and Bonanova in the same puzzle make me hope it's more difficult than that..

High expectations from your puzzles, Bonanova.

[bonanova]

6 4 7 8 3 7

8 2 5 1 5 6

3 -7- 8 6 4 8

8 6 5 3 7 6

5 4 7 -8- -2- 5

-7- 8 6 4 7 8

The posts above explained how we got to the numbers. I placed them where I did based on this logic: I didn't see any duplicate digits either horizontally, vertically, or diagonally. This is the only sequence that continues that pattern.

duplicate.

I would take that to mean two occurrences in a row/col/diag.

But that's unavoidable.

So ... what's your rule, exactly?

[Izzy]

No number may be repeated in one of the six spaces surrounding that number?

*edit* Or less than six. Depending on where the number is located. (Corners, sides, middle)

Edited November 24, 2008 by Izzy

[Guest]

duplicate.

I would take that to mean two occurrences in a row/col/diag.

But that's unavoidable.

So ... what's your rule, exactly?

It's probably fair to assume that by "duplicate" they meant "adjacent." That's the reasoning I used to get the same answer.

[bonanova]

Good collaborative job.

duplicate=adjacent. (eight or fewer, actually)

I wonder if it could have been done using circles, where "six or fewer" would apply?

Izzy, that's your task.

[Izzy]

6 4 7 8 3 7

8 2 5 1 5 6

37 8 6 4 8

8 6 5 3 7 6

5 4 78 7 5

2 8 6 4 7 8

Because when you look at the numbers one at a time, different numbers are also adjacent to certain numbers.

1 = 3,4,5,6,7,8

2 = 3,4,5,6,7,8

3 = 4,5,6,7,8

4 = 5,6,7,8

5 = 6,7,8

6 = 7,8

7 = 8

8 = anything?

And so if you put the numbers in the way I did, it works.

[Izzy]

I wonder if it could have been done using circles, where "six or fewer" would apply?

Izzy, that's your task.

What do you mean by "six or fewer"?

[Guest]

6 4 7 8 3 7

8 2 5 1 5 6

37 8 6 4 8

8 6 5 3 7 6

5 4 78 7 5

2 8 6 4 7 8

Because when you look at the numbers one at a time, different numbers are also adjacent to certain numbers.

1 = 3,4,5,6,7,8

2 = 3,4,5,6,7,8

3 = 4,5,6,7,8

4 = 5,6,7,8

5 = 6,7,8

6 = 7,8

7 = 8

8 = anything?

And so if you put the numbers in the way I did, it works.

This doesn't work because you say that 1 is adjacent to 7, but you don't say that 7 is adjacent to 1. This isn't possible. 1 and 7 aren't the only instances of this, but you get the point.

The only solution I can see is the one Bonanova already confirmed.

[Guest]

9 in the third row

6, 4 in the fifth row

7 in the last row

1. The sum of the first four numbers in a row will total the sum of the last four numbers in a row.

2. The sum of the first three rows will total the sum of the last three row.

[Guest]

I came up with 3 6 9 9 missing from patterns in the pairs of columns ?

look at the last 2 columns 10, 11, 12...

just a thought

[bonanova]

What do you mean by "six or fewer"?

What you meant.

It would apply for close-packed circles.

[Guest]

Since each number in the grid has the corresponding nubmerof occurrences, the missing numbers are 2,7,7,8.

The order of placement in the grid (placing from top to bottom and left to right) is 7, 2, 8, 7. This keeps identical numbers from being adjacent to one another and at least one 8 in each column.

[Izzy]

Woo, I've solved it. Well, depending on what you consider solved. There's about 4/5 pages of stuff, so as to not spam the thread, I'll put them all in spoilers.

Also, heh, proof I can't count. I meant "the 8 spots around it" not 6. But yeah, anyway:

At first I didn't know what you meant by close-packed circles. I experimented a bit with the 6x6 grid, which got me nowhere. It.. really didn't work. Because there are more 8's than any other number (by itself), I started with that.

Then I started working with the circles, and noticed that no way in hell were 6x6 rows of circles going to get me anywhere. The green paper clip represents an 8. The red represent all the places I can no longer put an 8 if the 8 is placed there. The area outlined in blue is the area we have to work with. (Ignore the squiggly circles. I was trying out different ways of doing stuff and didn't feel like redrawing.

So I got frustrated, and for the simpleness of it, I made the circles with no adjacent numbers being the same. Easy, fun, yeah.

Okay, so why does it have to be 6x6? It doesn't. These are my attempts with 1x36 (works), 2x18 (works, but didn't try it past the 8s) 3x12 (doesn't work), 4x9 (almost worked! I thought it had for a moment, but I messed up), and 6x6 (...).

After seeing how the 4x9 almost worked, I decided to modify it a bit. (No one said they had to be equal rows)

..and

Sort of. It depends on whether you consider it cheating or not.

Edited November 25, 2008 by Izzy

[Guest]

Since each number in the grid has the corresponding nubmerof occurrences, the missing numbers are 2,7,7,8.

The order of placement in the grid (placing from top to bottom and left to right) is 7, 2, 8, 7. This keeps identical numbers from being adjacent to one another and at least one 8 in each column.

i got this too.

[bonanova]

Woo, I've solved it.

Then I started working with the circles, and noticed that no way in hell were 6x6 rows of circles going to get me anywhere. The green paper clip represents an 8. The red represent all the places I can no longer put an 8 if the 8 is placed there. The area outlined in blue is the area we have to work with. (Ignore the squiggly circles. I was trying out different ways of doing stuff and didn't feel like redrawing.

Sort of. It depends on whether you consider it cheating or not.

Your spoiler 2 is more restrictive than just the 6 touching circles I had imagined.

Relaxing the requirement to just the 6 touching circles, your solution could be

neatened up to 5 rows of 7 7 8 7 7

8 7 5 6 7 8 5

.6 4 8 3 4 6 7

7 3 2 7 1 8 5 4

.6 8 6 5 2 7 3

8 5 7 4 8 6 8

Maybe 6x6 even.

Nice job.

[Izzy]

Relaxing the requirement to just the 6 touching circles, your solution could be

neatened up to 5 rows of 7 7 8 7 7

8 7 5 6 7 8 5

.6 4 8 3 4 6 7

7 3 2 7 1 8 5 4

.6 8 6 5 2 7 3

8 5 7 4 8 6 8

Maybe 6x6 even.

Nice job.

That's what spoiler #3 was.

Thanks.

[bonanova]

That's what spoiler #3 was.

Thanks.

I didn't read S3 closely enough.

Great!

[Guest]

Your spoiler 2 is more restrictive than just the 6 touching circles I had imagined.

Relaxing the requirement to just the 6 touching circles, your solution could be

neatened up to 5 rows of 7 7 8 7 7

8 7 5 6 7 8 5

.6 4 8 3 4 6 7

7 3 2 7 1 8 5 4

.6 8 6 5 2 7 3

8 5 7 4 8 6 8

Maybe 6x6 even.

Nice job.

Now I'm confused. Is that the solution? That rearranges the 6X6 grid as laid out by the town council and the original number sequence. How would I (as the technician) repair the board to its original state if I rearrange everything?

[Izzy]

Now I'm confused. Is that the solution? That rearranges the 6X6 grid as laid out by the town council and the original number sequence. How would I (as the technician) repair the board to its original state if I rearrange everything?

Hehe. No, it isn't. If you redirect somewhere on the second page, you'll see what we were doing. It was something completely unrelated. The answer should be in the 10th post or so.