Recent content by musicgold

Got it. Thanks! 👍 As shown below there are 8 duplicates. I also realized that there are actually 27 unique values of m and not 26. 27 unique values + 8 duplicates + 1 invalid = 36 combinations

While I found 26 possible values of m with the trial and error method, I wanted to find an elegant approach to solve such problems. I think the following equation represents the problem: m = 10d + 25q where ## 0 <= d < 9 ## and ## 0 <= q < 4 ## where d is the number of dimes and q...

Could you please explain how you reaching to ##14\leq S\leq 19## e - a has to be a negative number for S=19

Ahhh....sorry!:sorry: Thanks

Not sure what I am missing. :oldconfused: For S=15, a, d, f : 1, 3, 5 e = 15 - 3- 5 = 7 We are now left with 2, 4, 6, and 8. left leg: 1 + b + c + 3 = 15 -- no odd numbers left to make this work right leg: 1 + h + g + 5 = 15 -- no odd numbers left to make this work

I am able to get solutions for the following values of S: 19, 17, 16. The arrangement doesn't seem to work for S = 18, S=14, S =15. There appears to be some internal constraint that I am not able to see. I noticed the following constraints: 1. e must be < 9. We know that S = d+e+f . S...

I seem to get a solution for S=16. When a=1, d=7, f =4 The following values seem to be working out. a, b, c, d : 1, 2, 6, 7 a, h, g, f : 1, 8, 3, 4 e : 5

S = 12 + (d +f + a)/3 So (d +f + a) has to be a multiple of 3. Here are some possibilities. a d f 1 2 3 1 3 5 1 3 8 ... 5 6 7 ... 6 7 8 But again there are many possibilities. Do I have to test all of them out?

Thanks. I have corrected the equations.

First I tried to solve this with algebra, but there are not enough equations: a+ b + c + d + e + f + g + h = 36 S = 12 + (d +f + a)/3 ........... ( d +f + a has to be a multiple of 3) a + b + c = e + f a + h + g = d + e So I had to resort to the trial and error to find the solution...

Ah... Third possible exchange that would have exactly 3 different colors in each bag is: Move 1: P ( Arjun moves either the green, violet, or yellow ball to bag B) = 3/5 Move 2. P ( Becca moves the orange ball to bag A ) = 1/4 Move 3. P ( Arjun moves the orange ball to bag B ) = 1/5 P...

Here is my attempt. Beginning state: Bag B : B, B, O Bag A : R, R, G, V, Y Final state: Bag B: B, B, O, + G/V/Y Bag A: remaining balls First possible exchange that would have exactly 3 different colors in each bag is: Move 1: P ( Arjun moves either the green, violet, or yellow ball to...

Thank you all for helping me! 🙏

Thanks! I have reached up to the following equations. Not sure how to get the neat ##z=1\frac 23## from here. ##1599z^2 = 4625 -110z ## ##z^2 +0.07z-2.89=0 ##

My apologies! I am adding the correct picture here. I need to find the area of the garden path that runs diagonally across the garden. My attempt: I assumed that the sides of the triangular piece at the bottom left of the path are: 1, 1, and sqrt 2 yards. Area of the bottom right triangle =...