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Show that if p > 3 is a prime, then p ^2 ≡ 1 (mod 24)

 Jun 14, 2020
edited by guesttttt  Jun 16, 2020
 #1
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Matthew Casertano and Fox Chyatte make a series of bets. In each bet, Matthew sets the stake (the amount he wins or loses) at half his current amount of money. He has an equal chance of winning and losing each bet. If he starts with $256, find the probability that after 8 bets, he will have at least $50.  

 

Since there's an equal chance of winning or losing, let's alternate them.

Let's start with the worse case scenario, that Matthew loses the first bet. 

 

Bet Number      Wager      Win/Lose     Remaining Balance 

 

                                                                      256.00

      1                128.00         L                        128.00 

      2                  64.00         W                       192.00  

      3                  96.00         L                          96.00 

      4                  48.00         W                       144.00  

      5                  72.00         L                          72.00 

      6                  36.00         W                       108,00  

      7                  54,00         L                          54,00 

      8                  27,00         W                         81.00 

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 Jun 14, 2020
 #2
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Since, there is an equal chance of winning or losing any bet,

let's have Matthew lose four of those eight bets.  The first four

 

Bet Number      Wager      Win/Lose     Remaining Balance 

 

                                                                      256.00 

      1                128.00         L                        128.00 

      2                  64.00         L                          64.00 

      3                  32.00         L                          32.00 

      4                  16.00         L                          16.00 

      5                    8.00         W                         24.00  

      6                  12.00         W                         36.00 

      7                  18.00         W                         54.00  

      8                  27.00         W                         81,00 

 

So... 81 again.  Hmmm, I suspect there might be a pattern. 

.

 Jun 15, 2020
 #8
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I go to Texas for a week and when I come back the question is changed?  I will remember your name, guesttttt with 5 t's. 

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Guest Jun 21, 2020
edited by Guest  Jun 21, 2020
 #3
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Don't answer anything that this user posts. He posts problems from an online contest which is still going on, and he needs to be banned. This contest is called MBMT (Montegometry Blair Math Tournament)

 Jun 15, 2020
 #4
avatar+205 
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Hmmmm... how do you know this? Where is Blair, I never heard of this. If you can let me know that would be great. I would like to compete next year. Also, if its online I owuld suspect rules say that you may use nothing but your own brain... shame on this competitior

qwertyuiopasdfghjkl  Jun 15, 2020
edited by Guest  Jun 15, 2020
 #5
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https://mbmt.mbhs.edu/

Guest Jun 15, 2020
edited by Guest  Jun 15, 2020
 #6
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Wow he changed his question. MBMT please find this cheater

Guest Jun 16, 2020
 #7
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@qwertyuiopasdfhjkl, you hipocrite! You have already asked 2 of the questions from the tournament. https://web2.0calc.com/questions/helppppp_66 and https://web2.0calc.com/questions/help-now_10. Shame on you too!

Guest Jun 17, 2020

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