Math puzzles! - Printable Version

Math puzzles! - Printable Version

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Math puzzles! - shouri - 2011-11-08

rethic Wrote:7) 23?

ShinkuDragon Wrote:11:
hit 10*2 and 2*3
7*2 and 4*3
4*2 and 6*3
1*2 and 8*3

woo, new title
<-

Yes and yes Big Grin

If no one answers 8 through 10 by 8 pm Pacific... you guys can go ahead and answer 1 more each :3

Math puzzles! - shouri - 2011-11-09

Okay guys, no more answers so far~

Go ahead and have at em ( 7 through 10 )

Math puzzles! - ShinkuDragon - 2011-11-09

shouri Wrote:Okay guys, no more answers so far~

Go ahead and have at em ( 8 through 10 )

fixed, and i'm stumped here, lol, don't feel like doing them one at a time atm lol

Math puzzles! - Shidoshi - 2011-11-09

8) 103 but that took me a LOOOOOOOOOOOOONG time to find out. I just went through most 1-1 combos possible from 80 to 103 (since numbers before 80 are easy to make).

10) It's impossible to make a number that's not multiple of 3 with 3 numbers that are multiples of 3.
3n + 3m + 3k = 100, where n, m and k are integers.
n + m + k = 100/3 the sum of three integers can't be equal to a rational number.

For 4 triples the same reasoning goes,
3n + 3m + 3k + 3p = 100
n + m + k + p = 100/3, the sum of 4 integers can't be equal to a rational number.

Math puzzles! - shouri - 2011-11-09

Shidoshi Wrote:8) 103 but that took me a LOOOOOOOOOOOOONG time to find out. I just went through most 1-1 combos possible from 80 to 103 (since numbers before 80 are easy to make).
nope, and i just realized WHY... lololol... in darts it's REQUIRED that your very last shot is a double, no singles or triples. So you have to finish single/double, double/double, or triple double
10) It's impossible to make a number that's not multiple of 3 with 3 numbers that are multiples of 3.
3n + 3m + 3k = 100, where n, m and k are integers.
n + m + k = 100/3 the sum of three integers can't be equal to a rational number.
good good
For 4 triples the same reasoning goes,
3n + 3m + 3k + 3p = 100
n + m + k + p = 100/3, the sum of 4 integers can't be equal to a rational number.

8&9 still up for grabs :3

rofl, my bad guys.. read the bolded

Math puzzles! - ShinkuDragon - 2011-11-09

shouri Wrote:8&9 still up for grabs :3

rofl, my bad guys.. read the bolded

...judging by those rules and what you posted:

8) 1. you can't win
9) 1. you can't win.

there's got to be something else you forgotten though, otherwise this is a "did you read the notes?" question

Math puzzles! - HellenzSin - 2011-11-09

9)163
1-20: 2 miss, 1 dart hits 1-20
21-40: 1 miss, 1 dart hits 1-20, 1 dart hits 1-20
41-60: 1 dart hits 1-20, 1 dart hits 1-20, 1 dart hits 1-20
61-80: 1 miss, 1 dart hits 1-20, 1 dart hits 3x 1-20
81-100: 1 dart hits 20, 1 dart hits 1-20, 1 dart hits 3x 20
101-120: 1 dart hits 3x 20, 1 dart hits 2x 20, 1 dart hits 1-20
121-140: 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 1-20
141: 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 3x 7
142: 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 2x 11
143: 1 dart hits 50, 1 dart hits 3x 20, 1 dart hits 3x 11
144: 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 3x 8
145: 1 dart hits 3x 15, 1 dart hits 50, 1 dart hits 50
146: 1 dart hits 3x20, 1 dart hits 3x20, 1 dart hits 2x 13
147: 1 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 3x 9
148: 1 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 2x 14
149: 1 dart hits 3x 13, 1 dart hits 50, 1 dart hits 3x 20
150: 3 darts hit 50
151: 1 dart hits 50, 1 dart hits 3x 17, 1 dart hits 50
152: 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 2x 16
153: 1 dart hits 3x20, 1 dart hits 3x20, 1 dart hits 3x 11
154: 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 2x 17
155: 1 dart hits 3x 20, 1 dart hits 50, 1 dart hits 3x 15
156: 1 dart hit 3x 20, 1 dart hits 3x 20, 1 dart hits 3x 12
157: 1 dart hits 50, 1 dart hits 3x 19, 1 dart hits 50
158: 1 dart hits 3x 20, 1 dart hits 50, 1 dart hits 3x 16
159: 1 dart hits 3x20, 1 dart 3x20, 1 dart hits 3x 13
160: 1 dart hits 50, 1 dart hits 50, 1 dart hits 3x 20
161: 1 dart hits 3x20, 1 dart hits 50, 1 dart hits 3x 17
162: 1 dart hits 3x20, 1 dart hits 3x20, 1 dart hits 3x 14
163: can't. You can do everything with combinations of 20 and 50s, but this one. 2 darts 3x 20s, 43 left can't be done, prime. 2x 50s, 63 left, can't be done coz there is no 21. 3x 20 + 50, 53 left can't be done, prime.

Math puzzles! - shouri - 2011-11-09

ShinkuDragon Wrote:...judging by those rules and what you posted:

8) 1. you can't win
9) 1. you can't win.

there's got to be something else you forgotten though, otherwise this is a "did you read the notes?" question

T.T besides 1. Geez I'm really out of it. I keep forgetting to mention stuff D:

HellenzSin Wrote:9)163
1-20: 2 miss, 1 dart hits 1-20
21-40: 1 miss, 1 dart hits 1-20, 1 dart hits 1-20
41-60: 1 dart hits 1-20, 1 dart hits 1-20, 1 dart hits 1-20
61-80: 1 miss, 1 dart hits 1-20, 1 dart hits 3x 1-20
81-100: 1 dart hits 20, 1 dart hits 1-20, 1 dart hits 3x 20
101-120: 1 dart hits 3x 20, 1 dart hits 2x 20, 1 dart hits 1-20
121-140: 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 1-20
141: 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 3x 7
142: 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 2x 11
143: 1 dart hits 50, 1 dart hits 3x 20, 1 dart hits 3x 11
144: 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 3x 8
145: 1 dart hits 3x 15, 1 dart hits 50, 1 dart hits 50
146: 1 dart hits 3x20, 1 dart hits 3x20, 1 dart hits 2x 13
147: 1 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 3x 9
148: 1 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 2x 14
149: 1 dart hits 3x 13, 1 dart hits 50, 1 dart hits 3x 20
150: 3 darts hit 50
151: 1 dart hits 50, 1 dart hits 3x 17, 1 dart hits 50
152: 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 2x 16
153: 1 dart hits 3x20, 1 dart hits 3x20, 1 dart hits 3x 11
154: 1 dart hits 3x 20, 1 dart hits 3x 20, 1 dart hits 2x 17
155: 1 dart hits 3x 20, 1 dart hits 50, 1 dart hits 3x 15
156: 1 dart hit 3x 20, 1 dart hits 3x 20, 1 dart hits 3x 12
157: 1 dart hits 50, 1 dart hits 3x 19, 1 dart hits 50
158: 1 dart hits 3x 20, 1 dart hits 50, 1 dart hits 3x 16
159: 1 dart hits 3x20, 1 dart 3x20, 1 dart hits 3x 13
160: 1 dart hits 50, 1 dart hits 50, 1 dart hits 3x 20
161: 1 dart hits 3x20, 1 dart hits 50, 1 dart hits 3x 17
162: 1 dart hits 3x20, 1 dart hits 3x20, 1 dart hits 3x 14
163: can't. You can do everything with combinations of 20 and 50s, but this one. 2 darts 3x 20s, 43 left can't be done, prime. 2x 50s, 63 left, can't be done coz there is no 21. 3x 20 + 50, 53 left can't be done, prime.

You also missed the bolded where you're required to end in a double.

Here: official rules

Quote:Double-out: Players must reach "0" exactly by scoring in a double point value segment.

Quote:With 32 points to go, a double 16 will end the game. A single 16 will still leave 16 to go, which can be gotten by throwing a double 8, and so on down the line. If an odd number is thrown, another odd number is needed to get back to a double possibility. If one less or one more than the exact score is hit, the player must assume the same score he had at the end of his last turn. (This is called busting.) The rest of the rules hold.

aka, if you get down to 1 point... you bust and have to go back to the previous score you had.

Math puzzles! - Riyuran - 2011-11-10

8) 99

Spoiler

Math puzzles! - shouri - 2011-11-11

Riyuran Wrote:8) 99

Spoiler

2-41: 1/miss + 2x 1-20
42-60: 2-20 + 2x 20
61: 3x 7 + 2x 20
62: 2x 11 + 2x 20
63: 3x 13 + 2x 12
64: 2x 20 + 2x 12
65: 3x 13 + 2x 13
66: 3x 14 + 2x 12
67: 3x 19 + 2x 5
68: 3x 14 + 2x 13
69: 3x 15 + 2x 12
70: 3x 20 + 2x 5
71: 3x 15 + 2x 13
72: 3x 16 + 2x 12
73: 3x 19 + 2x 8
74: 3x 16 + 2x 13
75: 3x 15 + 2x 15
76: 3x 20 + 2x 8
77: 3x 17 + 2x 13
78: 3x 16 + 2x 15
79: 3x 19 + 2x 11
80: 3x 20 + 2x 10
81: 3x 17 + 2x 15
82: 3x 20 + 2x 11
83: 3x 19 + 2x 13
84: 3x 18 + 2x 15
85: 3x 15 + 2x 20
86: 3x 20 + 2x 13
87: 3x 19 + 2x 15
88: 3x 16 + 2x 20
89: 3x 19 + 2x 16
90: 3x 20 + 2x 15
91: 3x 17 + 2x 20
92: 3x 20 + 2x 16
93: 3x 19 + 2x 18
94: 3x 18 + 2x 20
95: 3x 19 + 2x 19
96: 3x 20 + 2x 18
97: 3x 19 + 2x 20
98: 3x 20 + 2x 19
99: Not possible! The highest number you can go with the second shot is 2x 20 = 40. So you need to get to 40 (or a lower even number) after the first shot. However, hitting 59 (or a higher odd number) with one shot isn't possible.
100: 3x 20 + 2x 20
101+: Not possible with only 2 darts.

Excellent, 99 is the correct answer Big Grin

Now do it with three darts Big Grin

(At the very least you already know what's possible with 2 darts, so no need to check those Big Grin

Math puzzles! - ShinkuDragon - 2011-11-11

shouri Wrote:Excellent, 99 is the correct answer

Now do it with three darts (At the very least you already know what's possible with 2 darts, so no need to check those

imma throw a dart in the dark and say 159

Math puzzles! - shouri - 2011-11-11

ShinkuDragon Wrote:imma throw a dart in the dark and say 159

And BULLSEYE! *ba dum tch*
that is indeed correct~ you can just triple 60 your way to anything before 159 by taking 99 and before for the last two darts. Excellent intuition! THIS IS THE TRUE ESSENCE OF MATH MUHAHAHAHAAHA! *cough* ahem~

12) Continue the sequence (If you've seen it, let everyone else suffer):

[just give me the next line]
1
11
21
1211
111221
312211
...?

Math puzzles! - ShinkuDragon - 2011-11-11

shouri Wrote:And BULLSEYE! *ba dum tch*
that is indeed correct~ you can just triple 60 your way to anything before 159 by taking 99 and before for the last two darts. Excellent intuition! THIS IS THE TRUE ESSENCE OF MATH MUHAHAHAHAAHA! *cough* ahem~

bawss. thanks ryu for doing all the hard work for me <3

and i've seen it, but can't remember exactly what the answer was >.<

Math puzzles! - Infernal - 2011-11-12

shouri Wrote:And BULLSEYE! *ba dum tch*
that is indeed correct~ you can just triple 60 your way to anything before 159 by taking 99 and before for the last two darts. Excellent intuition! THIS IS THE TRUE ESSENCE OF MATH MUHAHAHAHAAHA! *cough* ahem~

12) Continue the sequence (If you've seen it, let everyone else suffer):

[just give me the next line]
1
11
21
1211
111221
312211
...?

13112221

Math puzzles! - shouri - 2011-11-12

Infernal Wrote:13112221

Good good, each line just describes the previous one.

In the last line I posted we:

one 3, one 1, two twos, then two ones.
or
13,11,22,21

They're read off by groups not by total.

13) Let's have some fun :3 I would like you guys each to post up a single way to represent pi. Ingenuity wins this one (earlier ones receiving preference... since others will have the chance to see your creativity and just work to out do you... they better outdo you by a LOT to win).... so simple representations or re-writes of well known formulas will be frowned upon. This is a challenge of CREATIVITY. Everyone post your own creative way to represent pi. Just because someone else posted one doesn't mean you can't!

Edit: you do NOT have to represent pi exactly... approximations will do too... so long as they have a few digits of accuracy. As usual, please don't just look them up >.<

Math puzzles! - Holypie - 2011-11-12

Spoiler

Not very creative, but it's the best I can do on short notice.

Math puzzles! - ShinkuDragon - 2011-11-12

Spoiler

i... i just had to...

Math puzzles! - Shidoshi - 2011-11-13

Perimeter of an n sided polygon with a diameter of 1.

[Image: HEIFh.png]

The size of the side of this polygon can be calculated as 2*sin(360º/2n)*(1/2) = sin(180º/n), that is taking pitagoras on half of a pizza slice of the polygon.
The total perimeter of this polygon is n * sin(180º/n)

If we take the limit of n tending to infinity we have pi.
yay~

Math puzzles! - shouri - 2011-11-13

Okay, okay~ this is working so far~
Using equations that aren't as well known (physics, holypie)... and limits that also aren't obvious (Shidoshi, love the signature as well btw :3).... granted this shows up on wikipedia... hopefully you just learned it in class or something Big Grin

Let's see some more creativity, also... L> MOAR math people... get that creativity flowing~ You two (shidoshi/holypie) can post one more if you feel like it Big Grin

Math puzzles! - Shidoshi - 2011-11-13

That expression to get to pi is pretty common place (sorta), as a circle is just a polygon of infnite sides =D
I had solved that limit myself when I was studying calculus.

Meh, if I could remember there was this Fourrier series that you could use to get the value of pi as an infinite sum of sines and cosines, it's been too long though.

I'll see if I can think of something.