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# 5x5 statement table.

## Question

Statement table.

``````3 2 1 4 1
2 3 3 3 3
3 4 6 4 4
2 3 4 4 3
1 1 2 4 3
``````

Above 5x5 table contains numbers.
A number at each cell represent a statement.

x : This cell is surrounded by x True statements.

So if the number is 3 means the cell is surrounded by 3 True statement
We can say all statemets are false, but this is not what I want.
Some statements are true and some are not.

Create another 5x5 table with boolean (T/F) input,
to show which statements are true, and which statements are false.

example for 2x2 table.

``````1 3    ->  T F
0 1        F T
``````

I have checked there is only 1 solution.
Find the solution !

## Recommended Posts

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I wish there were some easier logic than trial-and-error (if there is, I missed it), but I have found the solution:

Spoiler

F F T F T
T T F F T
F T F T T
T T F T T
F F T F F

Edited by Logophobic
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I assume "surrounded by" means "adjacent to." So do diagonals count?

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@bonanova : yes diagonals count.

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Boolean Table of Statement Table above

T T F  F F
T T T T T
T T F T T
F T T T T
T T F T T

Are we looking for

T F T F T
F T F T F
T F T F T
F T F T F
F T F T F  ?

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If top-left corner (3) were true, then the three surrounding statements must also be true, and that implies that each of those is surrounded by at least three true statements. Since two of those statements claim to be surrounded by only two true statements, we have a contradiction. This proves the top-left corner to be false. There are others that can also be proven false, but I haven't had time to work out the full solution.

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it seems to me that

T F

F T

should be

1 2

2 1.

if you meant this...

``````3 2 1 4 1
2 3 3 3 3
3 4 6 4 4
2 3 4 4 3
1 1 2 4 3``````

cannot be solved.

F T  start for top left corner

T T

now 1 doesn't work.

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i think you mean...

x: this number is surrounded by no more than x true statements.

what the maximum number of trues you can have, and what would the board look like?

here's my attempt

Spoiler

F F F T F

T T F F F

F F T F F

F T F T T

F F F F T

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@ Phill, to make the question clear, I will explain the example

``````1 3    ->  T F
0 1        F T``````

(1,1) is true because the cell, is surrounded by 1 true statement (2,2)

(1,2) is false because the cell is not surrounded by 3 true statement, it only surrounded by 2 true statement (1,1) & (2,2)
(2,1) is false because the cell is not surrounded by 0 true statement, it surrounded by 2 true statement (1,1) & (2,2)
(2,2) is true because the cell, is surrounded by 1 true statement (1,1)

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Nice puzzle, jasen. Do you have more like this?

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@ bonanova

If you mean same puzzle with different numbers, you can create  It is easily, but maybe the solution is not unique.

if you mean different puzzle with T/F statement, I do not have, but I wiil create it, with another shape, maybe hexagon, triangle, or  etc.

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