Attacktix Riddle of the Day #3: Variations

[webhead817]

OK, this weeks riddle is a little different. This time around, I want to know:

How many different combinations are there for building a 100 point team?

The bonus question is the same for 50 points of back-ups.

I'm going to tell you up front, this number is very high. I don't need to know the specifics of the different teams, just how you came up with your numbers.

Have fun crunchin' them numbers!

[redemptionrocks]

more than two

[webhead817]

Oy, yes, more than two. In fact, if you haven't begun to do the math yet, I'm guessing the number would surprise most of you.

[malform]

This seems almost an impossible task.

I do have a spread sheet at home with all the figures and stats listed... Maybe that could help me figure out this little riddle of yours.

Oh, one question... Would these combos include the megas?

[webhead817]

You can skip the megas...think tournament legal 100 point teams only.

I'll give you all a big hint, it's "a very big number".

[malform]

Crud... I started crunching some numbers using megas... Ill tell ya, I went through the combos of 10's, 20's, 70+20+10, 60+40, 70+30, and 70+10; and came up with a number of 1071 combinations. Im not 100% sure Im going about this in the right way, but I think Im on the right track..... Any way, I have to go back and start over now.

[redemptionrocks]

Lol have fun I'm not doing this one

[Joe Manzo]

Combinations of 10 X 10point figures? OR combinations of 10X Jedi Knights being different than 10X Clone Troopers?

I guess with the answer being "very high" you mean by SPECIFIC characters!

[webhead817]

I mean like 10 x Jedi Knights is one variation, then 9 x Jedi Knights and 1 x Clone Trooper is another, Then 8 x Jedi Knights and 2 x Clone Trooper...

But I don't need it listed like that, just the total number, and how you came by it.

[Draaka]

29857205, How I got to it? Well I jkust hit some random buttons ;D

[webhead817]

Probably closer than you think to the total...

[webhead817]

OK, today I give an example, to give you an idea of what type of numubers we are talking about.

Let's say you just wanted to look at all of the different teams you could make using one each of a 10, 20, 30, and 40 point figure. This math is simple, take the total number of each different costed figure, multiply them all up. So, just for the above combination, you could have 425,040 different teams.

[webhead817]

webhead817 said:

So, just for the above combination, you could have 425,040 different teams.

To put that number in perspective, if you and a friend split all of those teams, and played quick ten minute games with each of them, playing each team only once, you would have to play for 35,337 hours, or about 4 years, to play one game with each of the different teams.

[YodaBreaker]

Yep, the math is simple, but the calculations are amazing.

By my reckoning, there are 21 different types of 100-point teams (listed by point values of figures; 40-pointers = F, 30-pointers = H, 20-pointers = W, 10-pointers = E; I've put the team webhead817 posted in italics to ensure we're calculating the same ways):

F*F*W = F² * H⁰ * W¹ * E⁰
F*F*E*E = F² * H⁰ * W⁰ * E²
F*H*H = F¹ * H² * W⁰ * E⁰
F*H*W*E = F¹ * H¹ * W¹ * E¹
F*H*E*E*E = F¹ * H¹ * W⁰ * E³
F*W*W*W = F¹ * H⁰ * W³ * E⁰
F*W*W*E*E = F¹ * H⁰ * W² * E²
F*W*E*E*E*E = F¹ * H⁰ * W¹ * E⁴
F*E*E*E*E*E*E = F¹ * H⁰ * W⁰ * E⁶

H*H*H*E = F⁰ * H³ * W⁰ * E¹
H*H*W*W = F⁰ * H⁰ * W⁰ * E²
H*H*W*E*E = F⁰ * H² * W¹ * E²
H*H*E*E*E*E = F⁰ * H² * W⁰ * E⁴
H*W*E*E*E*E*E = F⁰ * H¹ * W¹ * E⁵
H*E*E*E*E*E*E*E = F⁰ * H¹ * W⁰ * E⁷

W*W*W*W*W = F⁰ * H⁰ * W⁵ * E⁰
W*W*W*W*E*E = F⁰ * H⁰ * W⁴ * E²
W*W*W*E*E*E*E = F⁰ * H⁰ * W³ * E⁴
W*W*E*E*E*E*E*E = F⁰ * H⁰ * W² * E⁶
W*E*E*E*E*E*E*E*E = F⁰ * H⁰ * W¹ * E⁸

E*E*E*E*E*E*E*E*E*E = F⁰ * H⁰ * W⁰ * E¹⁰

Now, including gold-based and silver Tournament figures, there are 22 unique 10-pointers, 35 unique 20-pointers, 46 unique 30-pointers, and 12 unique 40-pointers. Hence, F=12, H=46, W=35, and E=22. Substituting into the above equations,

12*12*35 = 12² * 46⁰ * 35¹ * 22⁰ = 144*1*35*1 = 5,040
12*12*22*22 = 12² * 46⁰ * 35⁰ * 22² = 144*1*484*1 = 69,696
12*46*46 = 12¹ * 46² * 35⁰ * 22⁰ = 12*2116*1*1 = 25,392
12*46*35*22 = 12¹ * 46¹ * 35¹ * 22¹ = 12*46*35*22 = 425,040
12*46*22*22*22 = 12¹ * 46¹ * 35⁰ * 22³ = 12*46*1*10648 = 5,877,696
12*35*35*35 = 12¹ * 46⁰ * 35³ * 22⁰ = 12*1*42875*1 = 514,500
12*35*35*22*22 = 12¹ * 46⁰ * 35² * 22² = 12*1*1225*484 = 7,114,800
12*35*22*22*22*22 = 12¹ * 46⁰ * 35¹ * 22⁴ = 12*1*35*234256 = 98,387,520
12*22*22*22*22*22*22 = 12¹ * 46⁰ * 35⁰ * 22⁶ = 12*1*1*113379904 = 1,360,558,848
SUBTOTAL: 1,472,978,532

46*46*46*22 = 12⁰ * 46³ * 35⁰ * 22¹ = 1*97336*1*22 = 2,141,392
46*46*35*35 = 12⁰ * 46⁰ * 35⁰ * 22² = 1*2116*1225*1 = 2,592,100
46*46*35*22*22 = 12⁰ * 46² * 35¹ * 22² = 1*2116*35*484 = 35,845,040
46*46*22*22*22*22 = 12⁰ * 46² * 35⁰ * 22⁴ = 1*2116*1*234256 = 495,685,696
46*35*22*22*22*22*22 = 12⁰ * 46¹ * 35¹ * 22⁵ = 1*46*35*5153632 = 8,297,347,520
46*22*22*22*22*22*22*22 = 12⁰ * 46¹ * 35⁰ * 22⁷ = 1*46*1*2,494,357,888 = 114,740,462,848
SUBTOTAL: 123,574,074,596

35*35*35*35*35 = 12⁰ * 46⁰ * 35⁵ * 22⁰ = 1*1*1*52521875 = 52,521,875
35*35*35*35*22*22 = 12⁰ * 46⁰ * 35⁴ * 22² = 1*1*1500652*484 = 726,302,500
35*35*35*22*22*22*22 = 12⁰ * 46⁰ * 35³ * 22⁴ = 1*1*42875*234256 = 10,043,726,000
35*35*22*22*22*22*22*22 = 12⁰ * 46⁰ * 35² * 22⁶ = 1*1*1225*113379904 = 138,890,382,400
35*22*22*22*22*22*22*22*22 = 12⁰ * 46⁰ * 35¹ * 22⁸ = 1*1*35*54875873536 = 1,920,655,573,760
SUBTOTAL: 2,070,368,506,535

22*22*22*22*22*22*22*22*22*22 = 12⁰ * 46⁰ * 35⁰ * 22¹⁰ = 1*1*1*26559922791424 = 26,559,922,791,424

And adding all of the subtotals together, you get: 28,755,338,351,087! Thus, there are more possible Attacktix teams than there are dollars in the national debt.

Now that I've done this, I'll let someone else tackle the bonus question, with a hint that there are 6 different backup combinations.

[webhead817]

YB, I'll try and review your math, but it appears you have it, or a number close to it. As I've said, the number is ridiculous. If you consider that the number of back-ups combos will be a decent sized number, but that to come up with all possible tournament teams you would then multiply your number by the number of all possible back-ups...well, it's silly how big of a number you would be looking at.

The moral of the story? If you think you have tried everything with Attacktix, you haven't.