Printable View
Expand the grid to (5x5) still retaining only 4x4 dots and shifting them by one unit in both coordinates. Now, you have two points (0,4) and (4,0) which are not dots. The solution contains the line connecting these two points. This line connects three of the off main diagonal dots in the 4x4 dot matrix. It should be easy now! :) The solution does not retrace any line!Quote:
Originally Posted by Benny Lava
Benny Lava: When you gave your first solution you had (4,0) and (0,4) as two of the points. I thought you had the solution and asked you to check ! :)
Rajraj,Quote:
Originally Posted by rajraj
To me it looks impossible. Please post your complete solution.
Benny Lava,
I think you are trying to modify the solution you gave in the picture. Start all over again with the clue I gave! I am sure you will find it! If not I will post the solution! :)
Let me clarify whether my assumptions are right.Quote:
Originally Posted by rajraj
1. I am not allowed to retrace my path
2. Paths cannot overlap
3. It is a continuous path, i.e, I have to draw the path without lifting my pen.
Is that so?
Yes! Also you can not cross a line except at a dot ! :) When I said 'outside the box' to kirukan I meant going outside the 4x4 dot matrix ! :)Quote:
Originally Posted by Benny Lava
Andha naalavadhu point thaaney idikudhu :lol:Quote:
Originally Posted by rajraj
Anyway, my reasoning goes like this:
1. The first stroke you described (4,0) to (0,4) covers the 3 off-diagonal dots.
2. Since there are no intersections, drawing lines along both off-diagonals parallel to the anti-diagonal is ruled out but drawing the anti-diagonal is still a possibility. From here let us branch into two possibilities:
a) We draw an anti-diagonal: Now we cannot draw a main diagonal since it would intersect. Now consider the two middle points in main diagonal (1,2) & (2,1). To cover these points we require no less than 4 lines which leaves us only one line to cover other dots, definitely some would be left off.
b) We do not draw an anti-diagonal: To cover the same two middle points, we can only use vertical lines or connect by drawing main diagonal (lines perpendicular to it would intersect) Both the cases would have already consumed 4 strokes. It is impossible for the last stroke to cover rest of the dots.
So it seems like it is possible to connect the dots by just using 6 lines with above constraints. Am I missing something here? :oops:
. --o--- o----o---o <---- Start here at (4,4)
.....o.....o.....o.....o
.....o.....o.....o.....o
.....o.....o.....o.....o
..........................<--- from (0,4) draw a diagonal line to (4,0)
You have drawn two lines so far connecting 7 dots!
Now use only vertical and horizontal lines to complete the solution! :) ( Remember crossing a line at a dot is permissible! )
This vaathiyaar is very patient but a little bit demanding ! :lol: Not a great artist ! :)
Should be the same? A ball with diameter less than 8.28cm can pass through the gap. :huh:Quote:
Originally Posted by rajraj
Or should I think out of the box? :think:
If a large ball left a gap near the corner for a smaller ball, the smaller ball will also leave a gap near the corner for a still smaller ball ! :)Quote:
Originally Posted by GP
Now you don't have to think outside the box! The equations get a little more complex ! A little more stress ! :)