Puzzles- contd

[rajraj]

I can't figure it out, unless I am allowed to retrace my path along one of the lines. Could you post the solution please?

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!

[rajraj]

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 !

[Benny Lava]

I can't figure it out, unless I am allowed to retrace my path along one of the lines. Could you post the solution please?

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!

Rajraj,

To me it looks impossible. Please post your complete solution.

[rajraj]

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!

[Benny Lava]

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.

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?

[rajraj]

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.

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 !

[Benny Lava]

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.

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 !

Andha naalavadhu point thaaney idikudhu

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?

[rajraj]

. --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 ! Not a great artist !

[GP]

Radius of ball 20cm.

According to Pythagoras,
Distance between centre of ball and the edge of wall = 28.28 cm (sqrt(20^2+20^2)).
Of this 28.28cm, 20cm is already covered by the ball.

So a ball with diameter less than 8.28cm can pass through the gap.

Was a nice stress relief.

http://i38.tinypic.com/jazw2v.jpg

8.28 cm is the distance between the large ball and the corner where the wall meets the floor. What is the distance between that corner and the largest smaller ball that can go into that gap?

I am sorry I dd not scroll back to see any solutions posted !

Should be the same? A ball with diameter less than 8.28cm can pass through the gap.
Or should I think out of the box?

[rajraj]

Should be the same? A ball with diameter less than 8.28cm can pass through the gap.
Or should I think out of the box?

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 !

Now you don't have to think outside the box! The equations get a little more complex ! A little more stress !