[vivek.anand]

Hi...

Even i think the answer is 11* 9 = 99 roses...??:

[murthymsr]

Originally Posted by fultoo_bakar

instead plant them in hexagon.................the viability of 1 mt is being satisfied by the arrangement. the number of roses are coming out to be 132. what is the answer.......
atleast give the options.....................

Yes, in Hexagon or Rhombus formation, we can plant more.

Options as requested :

A) 99 B) 105 C) 95 D) 132 E) 80

[Rockeeze]

Originally Posted by murthymsr

Yes, in Hexagon or Rhombus formation, we can plant more.

Options as requested :

A) 99 B) 105 C) 95 D) 132 E) 80

very cool ques
honestly did it with the help of the hint

132

[murthymsr]

Originally Posted by fultoo_bakar

instead plant them in hexagon.................the viability of 1 mt is being satisfied by the arrangemet. the number of roses are coming out to be 132. what is the answer.......
atleast give the options.....................

Originally Posted by Rockeeze

very cool ques
honestly did it with the help of the hint

132

Can you explain how you got 132?
Thanks in advance.

[Rockeeze]

i hv drawn a rough sketch

plz correct me if im wrong

[Rockeeze]

hey

can we bring all of ur ques to concepts n fundas thread--------- where we can dissect each problem case by case

its an alrdy active thread n we cn contribute to the cause of learnin
lots of us r w8in for new members like u

thanks man
do revert back

[murthymsr]

Originally Posted by Rockeeze

i hv drawn a rough sketch

plz correct me if im wrong

Seen the sketch. But how does the arrangement total to 132? As I perceive from the sketch, the formation can be achieved by having 1 plant less in alternate rows and by having lesser inter row space than inter column space.

[murthymsr]

Originally Posted by Rockeeze

hey

can we bring all of ur ques to concepts n fundas thread--------- where we can dissect each problem case by case

its an alrdy active thread n we cn contribute to the cause of learnin
lots of us r w8in for new members like u

thanks man
do revert back

This is the second proposal for relocation of the thread contents and is for a very valid reason. This thread will not continue in the present location for the next problem, may be the moderator will decide on it's new location.

In the mean time, let me complete the current problem with the explanation tomorrow morning. I would prefer that the correct answer comes out properly explained from one of you, who have come close to the answer.

[murthymsr]

The Rose garden Problem

The question:

I want to grow the maximum possible number of rose plants in the available free space in my backyard which is of a rectangular shape and of size 8 metres X 10 meters. The horticulture expert advised me to ensure that the minimum distance between any two plants must be one metre for maximum yield of roses.

How many plants should I buy?

The Answer: 105

The Explanation:

8 meters X 10 meters @ 1 meter spacing - a quick response could be (8/1) * (10/1) = 80 plants.

A second thought would bring out the difference between plants (points) and spaces (lines). This would fetch a response of (8+1) * (10+1) = 9 * 11 = 99 plants.

As the area is rectangular, we will be tempted to stick to the rectangular configuration. Let us examine this configuration in detail. Take a plant from the middle region. We will have 4 plants around it in the East, West, North & the South directions, all the 4 are spaced ONE meter away from this plant. We will also have another set of 4 plants in the corners, each is at a spacing of (1+1)**1/2 = 1.414 meters. So in the corners, space is 'wasted', as 1 meter would have been sufficient.

Let us take the alternate formations. In the Hexagon layout, we will have 6 plants around each plant and ALL plants may be spaced at ONE meter from any plant in the middle region. But how to count the total plants in this configuration?

To achieve the hexagonal configuration, the distance between the rows will be 1.732/2=0.866 meters (Take one of the six equilateral triangles of the hexagon and calculate it's height). At this spacing, there will be 9 (8/0.866=9.237) row spacings, i.e., 10 rows. The 1,3,5,7,9th rows will have 10+1=11 plants and the 2,4,6,8,10 rows will have 10 plants. Total plants will be 5*11+5*10 =105 plants. This layout gives room for 6 more plants than the rectangular configuration.

There is another possibility. The plants may be spaced at 0.866 meters spacing along the 10 meters side and at 1 meter spacing along the 8 meter spacing. This gives a possibility of only 95 plants (calculate for yourself) and can be ignored.

So, the correct answer would be 105.

Two responses to this query indicated a possibility of 132 plants. If the same could be substantiated, the answer may have to be reviewed.

[Hans_Reiser]

<PART 1>
Though the solution is extensive its open-ended.
The solution to the problem should be like this
"There cant be more than X(i.e 105 or whatever) roses planted"
The problem I see with your hexagon based solution is that its more a trial and error based solution where you hope that the count is more than the earlier arrangement.
My compliments for reaching 105(which seems the largest), just that the proof isnt generic.

</END of PART 1>

<PART 2>
Most of you are aware of Project Euler.
Project Euler

I am struck to get the answer of the following
Problem:142

Find the smallest x + y + z with integers x y z 0 such that x + y, x y, x + z, x z, y + z, y z are all perfect squares.

Understanding from my analysis till now
1. Atleast 1 among X,Y,Z is greater than 100
{ using brute force method ...system generated numbers }
2. Dumb googling will not help you here
</END of PART 2>