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charliepatrick
charliepatrick
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Thanks for this post from:
Gialmere
December 1st, 2020 at 12:01:13 PM permalink
Quote: charliepatrick

...this is wrong...

Total perms =25*24*23/6 = 2300
For a triangle to have zero area the holes must be in the same line, diagonal or horizontal/vertical.

Diagonal 3-length lines - 4 of them, 1 perm = 4 combos
Diagonal 4-length lines - 4 of them, 4 perms = 16 combos
Diagonal 5-length lines - 2 of them, 10 perms = 20 combos
Vertical/Horizontal 5-length lines - 10 of them, 10 perms = 100 combos
Knight moves (each one only have 1 perm - e.g. A1 C2 E3) = 12 combos
(i) West to East - going up/North - three
(ii) West to East - going down/South - three
(iii) North to South - going right/East - three
(iv) North to South - going left/West - three

Total = 152 combos.

So P=152/2300.
USpapergames
USpapergames
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December 1st, 2020 at 2:20:17 PM permalink
Now here is an easy math puzzle ;) How far can you walk into a forest?

f/2 or half way
Math is the only true form of knowledge
charliepatrick
charliepatrick
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December 1st, 2020 at 2:27:49 PM permalink
Quote: USpapergames

Now here is an easy math puzzle ;) How far can you walk into a forest?

Assuming there's a clear boundary, then once you've fully crossed it you're inside. So not very far.

Of course if you didn't see it you might walk straight into a tree - gosh that hurt! And if you had come from a long way away, then it might be miles.

btw your "toes" will have come "far" to make it to "a forest" (anag).
USpapergames
USpapergames
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December 1st, 2020 at 2:31:42 PM permalink
Oh Charlie you make me laugh so hard! You do bring up some great points as usual. We could reframe this question so that it's a shopping mall & not a forest, yet the answer will still be the same ;)

The question isn't about how the traveler would know when he has reached the middle but rather how far is it possible for the traveler to be within the forest.
Math is the only true form of knowledge
Ace2
Ace2
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December 1st, 2020 at 8:09:50 PM permalink
Quote: USpapergames

Ok, so I have the actual answer! Looks like you guys need help with combination analysis.

You make me laugh long time
Itís all about making that GTA
Gialmere
Gialmere
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December 1st, 2020 at 8:47:28 PM permalink
Quote: ChesterDog


I counted 152 combinations that are colinear out of a total of 2300 leaving 2148 combinations to make triangles.

Probability of a triangle = 2148 / 2300 = 537 / 575 or approximately 93.39%


Quote: charliepatrick

Total perms =25*24*23/6 = 2300
For a triangle to have zero area the holes must be in the same line, diagonal or horizontal/vertical.

Diagonal 3-length lines - 4 of them, 1 perm = 4 combos
Diagonal 4-length lines - 4 of them, 4 perms = 16 combos
Diagonal 5-length lines - 2 of them, 10 perms = 20 combos
Vertical/Horizontal 5-length lines - 10 of them, 10 perms = 100 combos
Knight moves (each one only have 1 perm - e.g. A1 C2 E3) = 12 combos
(i) West to East - going up/North - three
(ii) West to East - going down/South - three
(iii) North to South - going right/East - three
(iv) North to South - going left/West - three

Total = 152 combos.

So P=152/2300.


Correct!

(With an assist from ThatDonGuy)


-----------------------------------

Have you tried 22 tonight? I said 22.
USpapergames
USpapergames
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December 2nd, 2020 at 9:00:29 AM permalink
Quote: Ace2

You make me laugh long time



Glad to know my confusion was amusing ;) And I was assuming all Charlie did wrong was calculating the combinations wrong and title it as permutations. Even assumed Donguy was attempting to solve the problem by calculating all the possible triangle combos before realizing he was just finding more exclusion outcomes (or more straight lines).

Question, what type of math puzzles come to mind when they are easy? To me, the definition of an easy math puzzle is a puzzle that requires no hidden information to solve, where all parts of the puzzle are straightforward & obvious. The puzzle could even take a very long time to solve as long as the average high school student could complete the puzzle with no help.

P.S. It's not like my combinatorial analysis was wrong either ;) Just didn't account for the extra straight-line outcomes which weren't obvious to me within the 2 minutes it took for me to complete my analysis lol. Don't forget I'm the only person to realize Charlie's permutation value was wrong & to come up with the correct combinations & permutation values for the problem.
Math is the only true form of knowledge
Gialmere
Gialmere
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December 2nd, 2020 at 9:04:27 AM permalink


The digits 0-9 are written down on ten 3x5 cards. The cards are then separated into five groups of two such that each group makes a prime number. For example...



How many different sets of five primes can you form this way?
Have you tried 22 tonight? I said 22.
charliepatrick
charliepatrick
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December 2nd, 2020 at 9:49:50 AM permalink
Quote: Gialmere

...How many different sets of five primes can you form this way?...

Logic said you didn't need to actually work out which 10-digits numbers were primes (obviously the ones ending in 5 can't be), but as the sum of the digits is a multiple of 9 (or 3) then none can be. Nice question! (btw it's almost a shame the total of the odd and even placed numbers aren't the same as that would make it divisible by 11 as well and give another chance to spot it.)
Edit: I've misread the question assuming you had to use all the cards to make a 10-digit number.
Last edited by: charliepatrick on Dec 2, 2020
CrystalMath
CrystalMath
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December 2nd, 2020 at 10:09:37 AM permalink
Quote: Gialmere


How many different sets of five primes can you form this way?




Each card must contain an odd and an even number, with the even preceding the odd.
05 is the only prime you can create with the number 5, so we only need to look at the ways to place the numbers 2,4,6,8 with 1,3,7,9.

We have the following possible primes:
41, 61
23, 43, 83
47, 67
29, 89

Because 41/61 choice will determine what number we use for 47/67, then we can never use the number 43.

This gets us down to:
41, 61
23, 83
47, 67
29, 89

So, it looks to me like there are only 4 choices:
05, 41, 67, 23, 89
05, 41, 67, 83, 29
05, 61, 47, 23, 89
05, 61, 47, 83, 29
I heart Crystal Math.

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