Puzzles- contd

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Originally Posted by Benny Lava

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Originally Posted by rajraj

Too much of stress relief ! :)

Try this one for a change:
You are given a 4x4 matrix of 16 dots. How can you connect them using maximum number of lines without crossing or retracing a line already drawn without lifting your pen? A line is a vertical or horizontal connection between two adjacent dots. No diagonal lines!

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The answer must be 15 and the solution seems to be easy, unless I am missing something here :confused2:

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Maximum number of lines? :) Your solution is the number of lines in a spiral connection! :)

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Originally Posted by Benny Lava

Ohh.. sorry.. I forgot to mention that limitation is 3 attempts.

Anyway, your answer is right. Now how can we separate 180 pounds of gravel into 40 pounds and 140 pounds using just 1 pound and 4 pounds standard measure? :D

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Assuming you have an old style scale with two pans:

180

90 90 (divide equally)

90 45 45 (divide 90 lb equally)

90 45 5 40 (weigh 5 lb from one 45 lb heap)

90+45+5 40

Be a little more clever! :)

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Originally Posted by rajraj

90 45 45 (divide 90 lb equally)

90 45 45+5 (add the 5 lb weight to one pan)
90 45 5 40+5 (remove 5lb material leaving the weights in the pan)
90 45 5 40 (remove the 5 lb weight from the pan)

90+45+5 40

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Quote:

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Originally Posted by rajraj

Quote:

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Originally Posted by Benny Lava

Quote:

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Originally Posted by rajraj

Too much of stress relief ! :)

Try this one for a change:
You are given a 4x4 matrix of 16 dots. How can you connect them using maximum number of lines without crossing or retracing a line already drawn without lifting your pen? A line is a vertical or horizontal connection between two adjacent dots. No diagonal lines!

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The answer must be 15 and the solution seems to be easy, unless I am missing something here :confused2:

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Maximum number of lines? :) Your solution is the number of lines in a spiral connection! :)

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17 :huh:
lets number the 16 dots as
01-02-03-04
05-06-07-08
09-10-11-12
13-14-15-16

Connection like this 02-06-05-01-02-03-04-08-12-16-15-14-13-09-10-11-07-03

I hope better solution exist.

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Originally Posted by GP

17 :huh:


I hope better solution exist.

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Try again ! I will give one for stress relief later ! :lol:

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Originally Posted by rajraj

Be a little more clever! :)

Quote:

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Originally Posted by rajraj

90 45 45 (divide 90 lb equally)

90 45 45+5 (add the 5 lb weight to one pan)
90 45 5 40+5 (remove 5lb material leaving the weights in the pan)
90 45 5 40 (remove the 5 lb weight from the pan)

90+45+5 40

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Excellent once again! :clap:

Quote:

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Originally Posted by rajraj

Quote:

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Originally Posted by Benny Lava

Quote:

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Originally Posted by rajraj

Too much of stress relief ! :)

Try this one for a change:
You are given a 4x4 matrix of 16 dots. How can you connect them using maximum number of lines without crossing or retracing a line already drawn without lifting your pen? A line is a vertical or horizontal connection between two adjacent dots. No diagonal lines!

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The answer must be 15 and the solution seems to be easy, unless I am missing something here :confused2:

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Maximum number of lines? :) Your solution is the number of lines in a spiral connection! :)

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Oh, sorry! When you said "without crossing" I thought it meant that only two edges can be drawn from a node.

And for your question, it can be solved easily if we apply Graph theory. The requirement is basically to construct an Euler's path through 16 nodes (number of edges are indeterminate at the moment).

For an Euler's path to exist, the graph must have zero or two nodes with odd number of edges. The maximum number of edges for a nxn matrix without considering Euler's path would be 2*n*(n-1). In this case it is 24. In such a setup the node properties is as such:

4 nodes with 2 edges
8 nodes with 3 edges
4 nodes with 4 edges

Clearly, the 8 nodes with 3 edges bothers us since we can not have more than 2 nodes as such. This means 6 nodes have to shed 1 edge each. If we want to maximize the number of edges, this can be accomplished by shedding merely 3 edges (shared by 6 nodes as a pair).

So the final solution is 24 - 3 = 21 edges.

Diagramatically, the 3 edges to remove are the middle edges of any three exterior sides. Like:

(1,2) to (1,3) &
(2,4) to (3,4) &
(4,2) to (4,3)

and other symmetrical variation of the same topology.

yellAm ok, yeppadi andha 21 lines connect pannuveengannu sollunga. :?

2-1-5-6-2-3-7-6-10-9-13-14-10-11-15-16-12-11-7-8-4-3.
Kirukan kirukkiya kodugal 21

is it right?

:clap: :clap: kirukan