Way back in my college days, I always feel excited every time I join engineering quiz competitions. I am also enjoying here in Steemit with the contests initiated by fellow Steemians. It feels me like I am still in college. The latest one I joined a big challenge was @smaeunabs’ budget principle challenge and I can’t believe I was able to win the 2nd place. Thanks to her!
Somehow, I found Sir @jaycee7viral’s challenge more mind baffling but yet entertaining. This post is in response to his Mind Games Contest # 1. So, let's get it on!
Question No. 1
AVERAGE LEVEL: “King’s Proposition”
You are a prisoner sentenced to death. The King offers you a chance to live by playing a simple game.
He gives you 50 red marbles, 50 black marbles and 2 empty bowls. He then says, “Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove One marble. If the marble is Red you will live, but if the marble is BLACK … you will die.”
How do you divide the marbles up so that you have the greatest probability of choosing a Red Marble?
MY ANSWER:
Arrange whatever I like because the odds of having a red marble is fair.
This is the simplest explanation. If the bowls are just to be switched or mixed without me knowing, then selecting a bowl and then a red marble at random is just the same selecting a red marble from a bowl containing 50 red and 50 black marbles.
Oh, you need a more complex explanation? Here it is!
There are two successive events and two mutually exclusive multiple events. The first event is to choose a bowl. So, the probability to have the first bowl is ½ and so for the other. The second event is choosing a red marble which depends upon how I placed the marbles into the bowls. But, these have another mutually exclusive event.
What are mutually exclusive events?
Mutually exclusive events are events that do not occur at the same time.
For example, I have to choose at random two marbles with the same color in a bowl that contains both 10 red and 20 black marbles. Then, the favorable events are: Red-Red or Blue-Blue. If choosing both red takes place, then blue-blue won’t happen any longer or if blue-blue take place, then red-red won’t happen anymore. But before any event has occurred, consider that all of them as favorable events.
By principle, the probabilities of mutually exclusive events must be added. So, suppose I am to place all the 50 red marbles in first bowl and 50 black in the second. Then the probability to get a red marble is:
P = ½
What if I’ll arrange them by 25-25 in each bowl? I mean, 25 blacks and 25 reds in one bowl and so as in the other. Then the probability is:
P = ½
Let’s try 10-40 and 40-10. Ten black and forty red marbles in the first bowl and 10 red and 40 black marbles in the second. Then the chance for you to get the red one is:
P = ½
All result is just ½ or 50%. I also made a calculation using an excel file to check the probability of each combination.
Therefore, I would arrange the marbles to wherever I like. By doing so, I could arrange them slowly like I am thinking just for me to give more time to feel the probably last moment of my life and give time in prayer that God may give favor in my life to get the red one. Hahaha.
Question No. 2
Hard Level – Sherwin Grey’s Riddle
There are five people. One of them shot and killed one of the other five.
- Dan ran in the NY City marathon yesterday with one of the innocent men.
- Mike considered being a farmer before he moved to the city.
- Jeff is a topnotch computer consultant and wants to install Ben’s new computer next week.
- The murderer had his leg amputated last month.
- Ben met Jack for the first time six months ago.
- Jack has been in seclusion since the crime.
- Dan used to drink heavily.
- Ben and Jeff built their last computers together.
- The murderer is Jack’s brother. They grew up together in Seattle.
Sherwin Grey arrived at the scene and immediately finds the murderer.
Who was the murderer?
Okay, let's be Sherlock!
Jeff is the murderer. Look at his alibi. He wants to install Ben’s new computer next week. But take note! They had built their last computers together.
Dan absolutely isn’t the murderer, is he? Dan surely couldn’t run in the marathon if he is the killer who has an amputated leg.
Ben just met Jack six months ago. So obviously, he is not the killer who is Jack’s brother. Speaking of Jack. Jack is the brother of the murderer. So, for sure he is not his brother, is he? That’s why he’s been secluded after the crime.
While Mike., Oh Mike? Who is he by the way? A once farmer who moved to the city. But where is he now? Dan, Jeff, Ben, and Jack are very alive. This could only mean that Mike is the one that is murdered.
Question No. 3
Final Level for Genius:
A man has to get a fox, a chicken, a sack of corn across a river. He has a rowboat, and it can only carry him and one other thing. If the fox and the chicken are left together, the fox will eat the chicken. If the chicken and the corn are left together, the chicken will eat the corn.
How does the man do it?
My Answer
The man does it by crossing the river seven times with the sequence of events in the following tables. The tables show the number of time the man has crossed the river. The thing or things left on the left side and the right side of the river and the thing with him on the boat.
The man brings the chicken and goes back for the fox. He brings the chicken again and leaves the fox behind. Then he ties the chicken and brings the sack of corn to go the other side of the river. Lastly, he goes back for the chicken.
| No. | Left | Boat | Right |
|---|---|---|---|
| 0 | man, fox, chicken, corn | ||
| 1 | fox, corn | man & chicken ==> | |
| 2 | fox, corn | <== man | chicken |
| 3 | corn | man & fox ==> | chicken |
| 4 | corn | <== man & chicken | fox |
| 5 | chicken | man & corn ==> | fox |
| 6 | chicken | <== man | fox & corn |
| 7 | man & chicken==> | fox & corn |
The man brings the chicken and goes back for the sack of corn. He brings the chicken again and leaves the sack of corn. Then he ties the chicken and brings the fox. Finally, he goes back for the chicken.
| No. | Left | Boat | Right |
|---|---|---|---|
| 0 | man, fox, chicken, corn | ||
| 1 | fox, corn | man & chicken ==> | |
| 2 | fox, corn | <== man | chicken |
| 3 | fox | man & corn ==> | chicken |
| 4 | fox | <== man & chicken | corn |
| 5 | chicken | man & fox ==> | corn |
| 6 | chicken | <== man | fox & corn |
| 7 | man & chicken==> | fox & corn |
As you see, the events differ starting the third sail in choosing what to bring. Either the fox or the sack of corn.
If you haven't read the original post! See it here.
Participate by using #mindgamescontest as the main tag.
Wow .. I'm totally blown away.. From your tables.. Great answer @fojgrance Goodluck :)
But I think that's not the answer, the probability is only 0.5, I got answer that would give 0.745. Haha. I'll post my solution a day before deadline. :)
Hahahhaah, goodluck master
Really @jaycee7viral? how bout the odds of winning this contest? hahaha what's the probability? Only you could answer that one. hahaha
Probability for you 0.0001. Mine is 0.9999. Wahahahahah.
Hahahahaa no
We will wait for the results for those who wins .. Haha lol.. Goodluck
Hahaha, yey!
I concede with my question number 1 answer! I didn't understand the problem well. hahaha. I thought the bowls must contain the same number of marbles. dang!
Engr @caratzky's answer and explanation are correct! Have you checked his post already? Check it here!
Great answers @fojrance. I agree with you on the second and third but not the first one. Good luck!
Oh, why u don't? pls do explain hahaha
Can I just say woman's intuition? Hahaha! I'd put half and half in each bowl. To still get 50/50 percent chance of survival.
Oh, isn't that the same as my answer too? I did show the 50-50 situation above and still got 50% the same as the other combinations. Hahaha.
Evidence kaayo @fojrance. Hehehe. Nalingaw ko. Yup, I realized that I still got the same conclusion you did. Pwd sad 1red in the rest of the black in one bowl that we will call the black bowl and 1 black in the rest of the red that we will call the red bowl. Nya let's hope and pray that when we get blindfolded, we get to pick the red bowl to get 96% chance of survival. Did I get it right?
No, cuz' we have to use all of the given marbles. :)
Yes I did, but the problem said that you'd have to choose one bowl when blindfolded. 😀
Grabeha ani oy. Dli man kaya sa akong brain hahahaha
kaya na uy. hahaha ikaw pa.
Hala mga bisya diay mu? Apir lol. :)
Oh yeah! hahaha. Maybe next time I'll initiate a mathematical bafflers challenge. haha.
Yaaaay nindot na ser! Sayun2 lang ser ha kanang makaya sa among brain hahahaha
hahaha ou ba. the rule will be different. ang pag post kay dapat on the 7th day. hahahaha
Sir, nglag akong utok brain haha
ahahaha why jade.