we have a circular dining table. we also have some bone china saucers(also circular). diameter of table top is fifteen times the diameter of saucer. we would like to place saucer on the table so that they neither overlap each other nor the edge of the table. how many can we place in this manner ?

• let the radius of table=r1
  let the radius of saucer=r2
  given that r1=15r2
  area of the table=(pi*r1*r1)
  area of the saucer=(pi*r2*r2)
  let the no of saucers=n
  therefore
  pi*r1*r1=n*pi*r2*r2
  => 15*15*r2*r2=n*r2*r2
  => n=225
• 11 years agoHelpfull: Yes(17) No(5)
• what's the correct solution?
• 11 years agoHelpfull: Yes(3) No(0)
• pls .....there is no clarity in answer.
• 11 years agoHelpfull: Yes(3) No(0)
• The most efficient arrangement is a
  "honeycomb" (hexagonal) packing.
  
  There is one saucer in the center,
  surrounded a "ring" by six saucers.
  
  The next ring contains 12 saucers.
  
  And the next has 24 saucers,
  followed by 48 saucers, and so on.
  With an arrangement with five rings,
  . . there are: .1 + 6 + 12 + 24 + 48 +
  96 =187 saucers.
  
  The table is 15 times the size of a
  saucer.
  There should be 7 possible rings.
  Perhaps part of the 7th ring extends
  beyond the table's edge
  Then there should be at least 6
  rings.
• 11 years agoHelpfull: Yes(2) No(3)
• ans : 47
  
  explanation:
  let us assume diameter of saucers be 2x unit.
  so, diameter of table is 15*2x=30x unit.
  
  now perimeter of the table = 2*pie*30x/2=30x*pie
  now if we place saucers on the table such that they neither overlap each other nor the edge of the table,then
  each saucer will take the space exactly equals to its perimeter.
  so,
  no of sauces can be placed in this manner is 30x*pie/2x=15*pie=15*3.14=47.10 =47
• 11 years agoHelpfull: Yes(1) No(6)
• What is right answer ?
• 11 years agoHelpfull: Yes(1) No(3)
• we can put 1 saucer at middle and put 6 arouind it
  so we get total 3 diameters of table wich all have 14 +1(middle one) saucer
  so total saucers=14*3 +1=43
• 11 years agoHelpfull: Yes(1) No(0)
• This question is taken from Shakuntala devi book(Puzzle)
  Official Answer is 187
• 9 years agoHelpfull: Yes(1) No(0)
• Let 15 saucers placed adjacent to each other in straight line makes the diameter of the table.
  if one saucer is such that it is at the center of the table and therefore there are 7 saucers on each side in the straight line.
  Now center saucer is surrounded by 6 saucers which includes the two saucer on both sides.
  So start arranging saucers around the center saucer and include saucers on the straight line and thus till the edge of the table.
  So total 763 saucers.
  
  
• 9 years agoHelpfull: Yes(1) No(0)