
By: kesterasd (offline) Thursday, September 12 2013 @ 02:29 AM CDT (Read 1862 times)



kesterasd 
Help me solve this question asap! Solve (b) and (c) please. Very urgent. (a) is done already. Thank you!

Newbie
Registered: 10/29/11 Posts: 4





By: kesterasd (offline) Thursday, September 12 2013 @ 02:31 AM CDT



kesterasd 
Help me solve please, anyone? I will be grateful to you for that if you do this before 15/9/13, Sunday. Thank you!

Newbie
Registered: 10/29/11 Posts: 4





By: echeewh (offline) Thursday, September 12 2013 @ 03:15 AM CDT



echeewh 
Hi <kesterasd>,
I suppose you have forgotten to attach / post your question here.
Best regards,
Edward

Active Member
Registered: 04/21/11 Posts: 627





By: kesterasd (offline) Thursday, September 12 2013 @ 10:11 AM CDT



kesterasd 
Is it attached now? Thanks for reminding.

Newbie
Registered: 10/29/11 Posts: 4





By: echeewh (offline) Thursday, September 12 2013 @ 08:10 PM CDT



echeewh 
Hey <kesterasd>,
//updated 26/9/13, 09 40
part (c)  reedited solution
//
Out of curiousity, I am wondering why are you not able to solve it or have the solution ready when you are the setter (as noted in your attachment). . Anyway, my worked solution is as follows:
Let n = Pattern number
Number of W triangles = [n(n+1)] / 2
Number of B triangles = [(n1)n] / 2
Total number of triangles = n × n
Number of triangles (1 stick) = [(n2)(n1)] / 2
Number of triangles (3 sticks) = 1
(a)
Pattern 5
Total triangles = 5 × 5 = 25
Number of triangles (1 stick) = (3 × 4) / 2 = 6
Number of triangles (2 sticks) = 25  6  1 = 18
Number of Sticks = (18 × 2) + 6 + 3 = 36 + 9 = 45
(b)
Pattern 100
Total triangles = 100 × 100 = 10000
Number of triangles (1 stick) = (98 × 99) / 2 = 4851
Number of triangles (2 sticks) = 10000  4851  1 = 5148
Number of Sticks = (5148 × 2) + 4851 + 3 = 10296 + 4854 = 15150
(c)
Shaded triangles = B triangles
Number of B triangles = [(n1)n] / 2
[(n1)n] / 2 = 210
(n1) × n = 420
20 × 21 = 420
n = 21
Hence, it is Pattern 21
=========
Trust this helps.
Do let me know if this is different from your <Answerkey> or if there's further clarification.
Cheers,
Edward

Active Member
Registered: 04/21/11 Posts: 627





By: kesterasd (offline) Thursday, September 12 2013 @ 08:56 PM CDT



kesterasd 
<echeewh>, the setter is not me, it is the person I share this account with. And he don't want to give me the answer key.
Anyway, thank you for helping me solve!

Newbie
Registered: 10/29/11 Posts: 4





By: echeewh (offline) Friday, September 13 2013 @ 06:51 PM CDT



echeewh 
Hey <kesterasd>,
Following is an <Alternative method> on the pattern for calculating the Number of Sticks. So this applies to (a) and (b) only.
Pattern 1 2 3 4 5
Triangles 1 4 9 16 25
Sticks 3 9 18 30
Total number of triangles = n × n
Number of W triangles = [n(n+1)] / 2
Number of B triangles = [n(n1)] / 2
Number of Sticks = Pattern + Triangles + [n(n+1)] / 2
= n + (n × n) + {[n(n+1)] / 2}
(a)
Pattern 5
Number of Sticks = 5 + (5 × 5) + [(5 × 6) / 2]
= 5 + 25 + 15 = 45
(b)
Pattern 100
Number of Sticks = 100 × (100 × 100) + [(100 × 101) / 2]
= 100 + 10000 + 5050
= 15150
(c)
Same as previous method.
=========
Trust this helps too...
Cheers,
Edward

Active Member
Registered: 04/21/11 Posts: 627





By: echeewh (offline) Wednesday, September 25 2013 @ 08:50 PM CDT



echeewh 
Hey <kesterasd>,
I have reedited the solution to part (c) of your question on 26/9/13, 09 40. My apologies for the mistake. Kindly review (c) on top.
Additionally I have found another alternative method (pattern) to calculate the Number of Sticks for (a), (b) as follows:
***  for alignment purpose
Pattern ************1 2 3 4 5
Triangles **********1 4 9 16 25
White Triangles ** 1 3 6 10
Sticks ************* 3 9 18 30
Number of Sticks = 3 × (White Triangles)
Number of White Triangles
= n(n+1) / 2
(a)
Hence, in Pattern 5,
White Triangles = (5 × 6) / 2 = 15
Number of Sticks = 15 × 3 = 45
(b)
in Pattern 100,
White Triangles = (100 × 101) / 2 = 5050
Number of Sticks = 5050 × 3 = 15150
==========
Trust this helps and any inconvenience caused is regretted.
Do let me know again if there are further clarifications.
All the best in your PSLE,
Edward

Active Member
Registered: 04/21/11 Posts: 627



