How many saucers on the table

Kaustubh Katdare · 2009-03-03T20:54:56+00:00

Imagine a round table with diameter equal to fifteen times the diameter of a saucer. Question: How many saucers can be accommodated on the table, without overlapping and not surpassing the table boundaries. Explain your answer.

How many saucers on the table

Kaustubh Katdare

Administrator

Updated: Oct 25, 2024

Views: 982

Imagine a round table with diameter equal to fifteen times the diameter of a saucer.

Question: How many saucers can be accommodated on the table, without overlapping and not surpassing the table boundaries.

Explain your answer.

0

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Replies

shalini_goel14

Member • Mar 3, 2009

Re: How many saucerrs on the table

Imagine a round table with diameter equal to fifteen times the diameter of a saucer.
Question: How many saucers can be accommodated on the table, without overlapping and not surpassing the table boundaries.

Answer: I guess the answer is 225 😕

No of saucers = (Area of table)/ (Area of each saucer)

Let us assume diameter of each saucer is D, then
Area of saucer A[sub]saucer[/sub]= ( pi * D[sup]2[/sup] )/4

diameter of table = 15D (As said in question), so

Area of table A[sub]table[/sub]= ( pi * (15D)[sup]2[/sup] )/4

No of saucers = A[sub]table[/sub] / A[sub]saucer[/sub]
= 225

Is this right? 😕

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Kaustubh Katdare

Administrator • Mar 3, 2009

Re: How many saucerrs on the table

You mean Two Twenty Five? :shock: !

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silverscorpion

Member • Mar 3, 2009

Re: How many saucerrs on the table

That wont be correct because, there will be gaps between the saucers. They cant be closely packed and so, ratio of areas wont give the correct answer.
As for the correct answer, I'm working it out and will post it after I figure it out..

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shalini_goel14

Member • Mar 3, 2009

Re: How many saucerrs on the table

@Scorpion thanks for the hint

I didn't took spaces into account.

Answer is 64 This time I think I am right. Right?

Explanation - See first coming from circumference - we can have 15 saucers at the circumfernce ok

How?
Circumference[sub]table[/sub] / Circumference[sub]saucer[/sub]
= pi * (15D) / pi * D
=15 saucers

Now again a circle of diameter 13D is created for you right?
How?
15D- D -D (each D from two ends of the diameter )
=13D

Then again applying same funda as above we can place 13 saucers in that circle

Continuing so...
We will get the series like following
15 + 13 +11 + 9 + 7+ 5 + 3 + 1
=Using AP formula ( (2 * a + (n-1) * d)* (n/2) )
= ( ( 2 * 1 + (8-1) * 2 ) * (8/2))
=64

I got answer as 64. Now I don't know how much correct it is ? 😔

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durga ch

Member • Mar 3, 2009

Re: How many saucerrs on the table

I am still stuck at 225 😔

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Saandeep Sreerambatla

Member • Mar 4, 2009

Re: How many saucerrs on the table

I have followed some empirical approach and found the answer to be 170.

I think this time its wrong.. i cant explain the explanation here will explain it tomorrow by trying it once again.
😎😎

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shalini_goel14

Member • Mar 4, 2009

Re: How many saucerrs on the table

Hey guys, last trial from my side . I missed something in my last explanation. 😔

Now my answer is 71. Is this right?

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Kaustubh Katdare

Administrator • Mar 4, 2009

Re: How many saucerrs on the table

Relax Shalini.

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silverscorpion

Member • Mar 5, 2009

Re: How many saucerrs on the table

I think shalini is trying all numbers from 1 to 225 in a trial and error method. 😀 😀

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shalini_goel14

Member • Mar 5, 2009

Re: How many saucerrs on the table

silverscorpion
I think shalini is trying all numbers from 1 to 225 in a trial and error method. 😀 😀
Ha ha ha..😁 Atleast I was trying something and what you are doing waiting for a table whose diameter is 15 times the diameter of saucers and then try it? Tell? 😁

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durga ch

Member • Mar 5, 2009

Re: How many saucerrs on the table

168

the diametre is 15 times the diameter of the small bowl.
ie on diamter we can accomodate 15 bowls.
ie centre one bowl and on each side of the centre bowl 7 .

same is on the second perpendicular diameter

to have maximum utilisation of space i would prefer to put second row of bowls between 2 bowls of first row.

now I have this would be only for counting no of rows i can accomodate
*
*
*
*
*
*
*
* * * * * * * * * * * * * * * *
*
*
*
*
*
*
*
so I can arrange 7 rows above and below
so counting 15+14+13+12+11+10+9=84
on both sides = 168

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Saandeep Sreerambatla

Member • Mar 6, 2009

Re: How many saucerrs on the table

I too followed the same approach.
i got the answer is 171 😎😎

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silverscorpion

Member • Mar 6, 2009

Re: How many saucerrs on the table

durga
168

the diametre is 15 times the diameter of the small bowl.
ie on diamter we can accomodate 15 bowls.
ie centre one bowl and on each side of the centre bowl 7 .

same is on the second perpendicular diameter

to have maximum utilisation of space i would prefer to put second row of bowls between 2 bowls of first row.

now I have this would be only for counting no of rows i can accomodate
*
*
*
*
*
*
*
* * * * * * * * * * * * * * * *
*
*
*
*
*
*
*
so I can arrange 7 rows above and below
so counting 15+14+13+12+11+10+9=84
on both sides = 168
Seems you made a mistake. Following this approach, we'll get the answer to be,

n = 15 + 2*(14+13+12+11+10+9+8)
n = 15 + 154
n = 169.

because, the center row only contains 15 saucers. There are seven rows above and below the canter row, and so, seven numbers from 15 should be included.
You left eight twice, and included an extra 15. So, you got 168.
Of course, i dont know if this is the correct answer. I just corrected the mistake in your approach.

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durga ch

Member • Mar 7, 2009

Re: How many saucerrs on the table

dude. you are absolutely correct. I messed up with calculation. Thanks !!😀

Biggie high time you say out the answer 😛

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Differential

Member • Mar 8, 2009

Re: How many saucerrs on the table

169. Am I right??

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shalini_goel14

Member • Mar 8, 2009

Re: How many saucerrs on the table

shalini_goel14
@Scorpion thanks for the hint

I didn't took spaces into account.

Answer is 64 This time I think I am right. Right?

Explanation - See first coming from circumference - we can have 15 saucers at the circumfernce ok

How?
Circumference[sub]table[/sub] / Circumference[sub]saucer[/sub]
= pi * (15D) / pi * D
=15 saucers

Now again a circle of diameter 13D is created for you right?
How?
15D- D -D (each D from two ends of the diameter )
=13D

Then again applying same funda as above we can place 13 saucers in that circle

Continuing so...
We will get the series like following
15 + 13 +11 + 9 + 7+ 5 + 3 + 1
=Using AP formula ( (2 * a + (n-1) * d)* (n/2) )
= ( ( 2 * 1 + (8-1) * 2 ) * (8/2))
=64

I got answer as 64. Now I don't know how much correct it is ? 😔

Can't believe it , it was me giving such a non sense explanation. (Don't know where was my brain at that time 😕 )

Guys !! Please ignore it completely.:sshhh:

I guess durga, Scorpion and Differential are right ?

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arsh86

Member • Mar 21, 2009

i think it is 173.
hello
Big K...........
tell us the right ans...

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Kaustubh Katdare

Administrator • Mar 21, 2009

I don't know the answer. If someone can logically explain the answer and everyone else agrees - we'll have the right answer.

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raj87verma88

Member • Mar 21, 2009

What? But you posted the question.

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durga ch

Member • Mar 21, 2009

aha!
Thats what. all have almost given up with the answer anf BIggie throws the bolt saying he doesnot know the answer!
mean!

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Saandeep Sreerambatla

Member • Mar 21, 2009

The answer given by Silver scorpion is correct logically too.

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