Puzzles- contd

Quote:

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Originally Posted by NM

vendikkai innum saapadanum-pOla

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Yes! Lots of it! Try different reasoning ! :lol:

NM: (n+1)x(n+3) = [(n+2) -1] x[(n+2) +1 ]
= [ (n+2)^2 - 1 ]

Does this give you a clue? :)

Quote:

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Originally Posted by rajraj

NM: (n+1)x(n+3) = [(n+2) -1] x[(n+2) +1 ]
= [ (n+2)^2 - 1 ]

Does this give you a clue? :)

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hi uncle -
are you saying its wrong?
I thought the sequence should be
3, 8, 15, 24, 35, 48, 63,80, 99, 120 etc......
so the number that's odd is 25 :(

Quote:

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Originally Posted by NM

Quote:

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Originally Posted by rajraj

NM: (n+1)x(n+3) = [(n+2) -1] x[(n+2) +1 ]
= [ (n+2)^2 - 1 ]

Does this give you a clue? :)

---

hi uncle -
are you saying its wrong?
I thought the sequence should be
3, 8, 15, 24, 35, 48, 63,80, 99, 120 etc......
so the number that's odd is 25 :(

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I did not say it was wrong! I asked for different reasoning! You have it in the series you gave! What is common to those numbers? :) To make it plain what is the relationship between 25 and 24 ? :)

oooooh! appadiya - its always (the perfect square of a number - 1) .... sorry - didn't quite understand was was required.

(0+2)^2 - 1 = 3
(1+2)^2 - 1 = 8
(2+2)^2 - 1 = 15 etc

ippO naan elementary-thaana illa foundtaion-a? :lol: :lol:

Quote:

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Originally Posted by NM

ippO naan elementary-thaana illa foundtaion-a? :lol: :lol:

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I will tell you after ten more puzzles! :lol: A professor has to give enough tests before awarding a grade ! :lol:

You always try for a simple solution ! :)

Another simple one with numbers ( 4x4 matrix of 16 numbers):


3 7 2 6

4 1 5 8

6 4 5 3

5 6 x 1


What is x ?

6.
Both row-wise and column-wise the sum is 18.
ivlO semipleA kuduthirukka vEndaam.
naan play school ku eligibleA?

Quote:

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Originally Posted by GP

ivlO semipleA kuduthirukka vEndaam.

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Stress relief ! :lol:

For the clock puzzle,

The repairman has put minute hand on the place of seconds hand.

Another simple one for stress relief. :wink:

How can you split Rs. 1.15 in six denominations so that you can not have change for one rupee, 50 paise, 25 paise, 10 paise and 5 paise?

I leave this to those in India to solve! :) I have not handled Indian coins in a long time! I don't even remember what denominations are available now ! :)

5 Paise, 10 paise, 20 paise, 25 paise, 50 paise and one rupee denominations can be used. (1 Rupee = 100 paise)

50+25+10+10+10+10?

:clap: Kirukkan :thumbsup:

Quote:

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Originally Posted by kirukan

Quote:

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Originally Posted by Benny Lava

11826^2 = 139854276
30384^2 = 923187456

Below is the OML(optimization modeling language) model I wrote to arrive at this:

Code:

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Model
[
Decisions[
Integers[1,9],a,b,c,d,e,f,g,h,i
],
Decisions[
Integer[10000,31622],y
],

Constraints[
a + b*10 + c*100 + d*1000 + e*10000 + f*100000 + g*1000000 + h*10000000 + i*10000000 == y*y
Unequal[a,b,c,d,e,f,g,h,i],
],

Goals[
Minimize[a + b*10 + c*100 + d*1000 + e*10000 + f*100000 + g*1000000 + h*10000000 + i*100000000]
]
 
]

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I think this is one hellova tool from Microsoft! :2thumbsup: :2thumbsup: Very simple and easy to solve optimization problems using this. Others interested may try this from here:

http://code.msdn.microsoft.com/solverfoundation

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Kirukans kirukkal code :wink: for getting the same result
--TSQL MSSQL2005

Code:

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declare @num bigint ,@min bigint ,@max bigint , @sqr bigint,@total int,@rnd varchar(9),@con varchar(9),@cnt int
set @sqr=0

set @num=10000
set @min=0
set @max=0
while(@num<100000)
begin
        set @num=@num+1
        set @sqr=power(@num,2)
        set @rnd= ltrim(str(@sqr))
        if(len(@rnd)>9) break
        set @total=1
        if (charindex('0',@rnd)>0) continue
        set @con=''
        set @cnt=1
        while (@cnt<10)
        begin
                if(charindex(substring(@rnd,@cnt,1),@con)>0)
                begin
                        set @total=0
                        break
                end
                else
                set @con=@con+substring(@rnd,@cnt,1)
                set @cnt=@cnt+1
        end
                if(@total=1)
                begin
                        if(@min=0) set @min=@num
                        set @max=@num
                end
end
select @min as Minimum,convert(bigint,power(@min,2)) Min ,@max as Maximum,convert(bigint,power(@max,2)) Max

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-

Kirukkan

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Splendid! :clap:

I am no good at programming, just script some timepass kirukkals but you call yours a kirukkal!! :shock: You have coded everything from scratch!

Anyway this must be much quicker since we just have to square 9000 numbers and check if they have unique digit, whereas my method would have to undergo at least 9! iterations to arrive at solution! :thumbsup:

Quote:

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Originally Posted by GP

For the clock puzzle,

The repairman has put minute hand on the place of seconds hand.

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idhu correct thaana?

Quote:

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Originally Posted by GP

Quote:

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Originally Posted by GP

For the clock puzzle,

The repairman has put minute hand on the place of seconds hand.

---

idhu correct thaana?

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Yes.. yes! Forgot to reply.. Good work! :2thumbsup:

This one is pretty simple!

"A half is a third of it. What is it?" :P

1.5.
half is one third of 1.5.
:huh:

Quote:

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Originally Posted by GP

idhu correct thaana?

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Karnan film dialogue, Krishna to Arjuna: "naan thaan konnEn, naandhaan konnEn!" :lol2:

Quote:

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Originally Posted by NOV

Quote:

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Originally Posted by GP

idhu correct thaana?

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Karnan film dialogue, Krishna to Arjuna: "naan thaan konnEn, naandhaan konnEn!" :lol2:

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:shock: comparing me to Lord Krishna.

Quote:

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Originally Posted by GP

1.5.
half is one third of 1.5.
:huh:

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Yes! Avlo thaan.. :)

Try this one.

You have 180 pounds of gravel and a balance. You need to weigh out 150 pounds and 30 pounds of gravel. You only have 6 pound and 9 pound standard weights. How would you do that?

Quote:

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Originally Posted by GP

Quote:

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Originally Posted by NOV

Quote:

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Originally Posted by GP

idhu correct thaana?

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Karnan film dialogue, Krishna to Arjuna: "naan thaan konnEn, naandhaan konnEn!" :lol2:

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:shock: comparing me to Lord Krishna.

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:P
It was Arjuna who said that dialogue with Krishna mimicking him. :P
Karnan died earlier; arjuna's last arrow just confirmed his death. :P

Quote:

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Originally Posted by Benny Lava

Quote:

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Originally Posted by GP

1.5.
half is one third of 1.5.
:huh:

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Yes! Avlo thaan.. :)

Try this one.

You have 180 pounds of gravel and a balance. You need to weigh out 150 pounds and 30 pounds of gravel. You only have 6 pound and 9 pound standard weights. How would you do that?

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any restriction on number of times the balance can be used or maximum weight the balance can hold?

Weigh 30 pounds of Gravel in 2 attempts using 15 pound (6+9) standard weight. Remaining should be 150 pounds. :|

Should we also check whether the remaining quantity has 150 pounds of Gravel?
if yes,
1) weigh 45 pounds gravel using 15 pound standard weight and 30 pound gravel (that was already weighed). We now have 15 pound standard weight, 30 pound gravel, 45 pound gravel.
2) Weigh 90 pound gravel using 15 pound standard weight, 30 pound gravel, 45 pound gravel. We now have 15 pound standard weight, 30 pound gravel, 45 pound gravel, 90 pound gravel.
3) Check whether the remaining gravel weighs 15 pound using 15 pound standard weight.

2 steps to get 30 pound gravel and 5 steps to confirm whether the remaining gravel weighs 150 pound.

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!

Quote:

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Originally Posted by GP

Weigh 30 pounds of Gravel in 2 attempts using 15 pound (6+9) standard weight. Remaining should be 150 pounds. :|

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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

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:

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! :)

Quote:

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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! :)

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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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.

Quote:

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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:

Quote:

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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!

---

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

---

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