Hidden Wallet of Question Mark

After recent events, Question Mark is annoyed with his brother, Skid Mark. Skid thought it would be funny to hide Question's wallet. 

He told Question that he would get it back if he finds it. So, first off, Skid laid five colored keys in a row. One of them is a key to a room where Skid is hiding Question's wallet. 

Using the clues, can you determine the order of the keys and which is the right key? 

Red: This key is somewhere to the left of the key to the door. 

Blue: This key is not at one of the ends. 

Green: This key is three spaces away from the key to the door (2 between).

Yellow: This key is next to the key to the door. 

Orange: This key is in the middle.

Logical Steps to know the RIGHT key are here!

Key to Get Question Mark's Wallet

Why to find Question Mark's Wallet?

Let's take a look at the given clues once again - 

1.Red: This key is somewhere to the left of the key to the door. 

2.Blue: This key is not at one of the ends. 

3.Green: This key is three spaces away from the key to the door (2 between). 

4.Yellow: This key is next to the key to the door.

5.Orange: This key is in the middle. 

Now, let's draw a table of locations and color of keys as below - 

From Clue No.5, it's clear that the orange key is in the middle.

As per Clue No.3, the green key is three spaces away from the key to the door (right key) (2 between). So, the possible positions of green and right keys
are -

Since as per Clue No.4, yellow key is next to the key to the door, the key to the door can't be positioned at 2 or 5. Hence, it might be positioned at 1 or 4 with Green key at 4 or 1.

But as per Clue No.1, red key is somewhere to the left of the key to the door. For that, the right key can't be positioned at 1 as in that case, no position would be left for the red key as per clue.

Hence, Green key must be at 1 and right key at 4.

 
And now as per Clue No. 4, yellow key is next to right key.

As per Clue No.1, red key is somewhere left to the right key,hence it must be at position 2.

And as per Clue No.2, blue isn't at either end. Rather blue key is the only key left. So, the position left for it is position 4 which is of Right key. Hence, Blue key itself is RIGHT key to the door of room where Question Mark's wallet is placed.

Bags of Marbles - Puzzle

There are three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble. 

You pick a random bag and take out one marble, which is white. 

What is the probability that the remaining marble from the same bag is also white?

Here is the solution! 

Bags of Marbles Puzzle - Solution

What is the puzzle?

Well, the probability that the second marble is also white should be 1/2 not 2/3 as most of answers to this puzzle claims!

There is no way that you have picked up the bag B having 2 black marbles since the first marble you have drawn is white. Hence, you must have picked up Bag A or C.

Claim :  

You chose Bag A, first white marble. The other marble will be white

You chose Bag A, second white marble. The other marble will be white

You chose Bag C, the white marble. The other marble will be black

So 2 out of 3 possibilities are white.


Hence, 2/3 is the probability of the second ball is also white.


Correct Approach :

The probability of the particular bag being picked randomly is 1/3 initially. Once the bag picked and since the marble drawn from it is white, the bag must be either A (2 whites) or C (1 white, 1 black).

The probability that the bag you picked is A (or C) must be 1/2 and hence the probability that second marble is also white (or not white) has to be also 1/2.

All You Need to Know About New IPL 2022 Format

After having magnificent Mega Auction for 15th edition of IPL i.e. TATA IPL 2022, BCCI announced new interesting format for the edition. Why?

Addition of 2 new teams:

If double round-robin format to be followed directly then total number of matches would be 2 x (9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1) = 90. Each team will be playing 18 matches.

That's massive jump of 34 matches from 56 matches when there were only 8 teams. 2 x ( 7 + 6 + 5 + 4 + 3 + 2 + 1) = 56. That can make tournament very monotonous & lengthy for the obvious reason.

What's the new format?

Now all 10 teams are divided into 2 groups having 5 teams each. But they are not randomly placed in groups. Their performances (except of 2 new teams) so far are counted for the purpose.

First of all old 8 teams are ranked from 1 to 8 depending on their success in IPL history so far with 2 new teams placed randomly at bottom. 

1. Mumbai Indians (5 titles)

2. Chennai Superkings (4 titles)

3. Kolkata Knight Riders (3 titles)

4. Sunrises Hyderabad (1 title + 1 runner up; 6 playoffs)

5. Rajasthan Royals (1 title ; 4 playoffs)

6. Royal Challenger Benglore (3 runner up; 6 playoffs)

7. Delhi Capitals (1 runner up ; 6 playoffs)

8. Punjab Kings (1 runner up ; 2 playoffs)

9. Lucknow Supergiant 

10. Gujrat Titans

So Mumbai Indian winning title 5 times ranked first followed by Chennai Superkings winning 4 times. KKR winning the title twice ranked 3rd in the list.

Since SRH & RR won title once but SRH being managed to qualify for playoffs 6 times, it is ranked above RR. RCB being runner up 3 times ranked above DC. Though DC & PBKS runner up for 2 times DC had managed to qualify for playoffs more times than PBKS; hence ranked above PBKS.

So WINNER, RUNNER-UP, PLAYOFFS are the 'measuring' criteria in order for success of any IPL team.

Teams Allocation in group : 

Teams ranked 1, 3, 5, 7, 9 are allocated in GROUP A while teams having rank 2, 4, 6, 8, 10 are placed in GROUP B like below.

IPL 2022 GROUP A Teams:

1) Mumbai Indians (MI)

2) Kolkata Knight Riders (KKR)

3) Rajasthan Royals (RR)

4) Delhi Capitals (DC)

5) Lucknow Super Giants (LSG)

IPL 2022 GROUP B Teams:

1) Chennai Super Kings (CSK)

2) Sunrisers Hyderabad (SRH)

3) Royal Challengers Bangalore (RCB)

4) Punjab Kings (PBKS)

5) Gujarat Titans (GT)

Matches : 

Each team in group will play 2 matches with the teams of the same group like double round-robin. So there will be total 2 x 2 (4 + 3 + 2 + 1) = 40 such matches among group teams only. Additionally, each team from one group will play 2 matches with team having same rank in other group & 1 match each with rest of 4 teams of other group. In that way, total 5 x (2 + 1 + 1 + 1) = 30 more matches to be played. 

So total 40 + 30 = 70 matches to be played at the group stage.

Logic behind the format :

The most successful team of GROUP A is MI & that of GROUP B is CSK. The most successful team of GROUP A is playing 2 matches against the most successful team of GROUP B (reward for being successful 😉) & 1 match against each of 4 remaining team. So each team will be playing (2 x 4) + 2 + 1 + 1 + 1 = 14 matches.

Similarly, the second most successful team of GROUP A will play 2 matches against the second most successful team of GROUP B & 1 match against each of 4 remaining teams.

Apart from those above matches each team is playing twice against each of own group member team.

For example, MI will play twice against own group teams & also twice against CSK of other group & once against rest 4 teams (SRH, RCB, PBKS, GT). 

GROUP A's third ranked RCB will play twice against own group teams & also twice against 3rd ranked RR in other group & once against rest of 4 teams (MI, KKR, DC, LSG) belonging to other group.

This way, each team of group will be playing 4 less matches compared to full double round-robin format (without groups). Hence, 5 x 4 = 20 less matches (i.e.70) compared to 90 matches of full double round Robin.

Playoffs/Semi Final/Final : 

BCCI hasn't announced the format of playoffs. 

In IPL 2011 too there were 10 teams competing & matches were played exactly like above format but at the time teams randomly placed in 2 groups. 

Top 4 teams among 10 (irrespective of groups) having more points and/or better NRR qualified for playoffs. Qualifier 1 played between top 2 with winner reaching to the final directly. Eliminator 1 played between teams ranked 3rd & 4th. Winner of Eliminator 1 played against loser of Qualifier 1 in match named Eliminator 2. Winner of this Eliminator 2 played against winner of Qualifier 1 in Final.

How long was he walking?

Every day, Jack arrives at the train station from work at 5 pm. His wife leaves home in her car to meet him there at exactly 5 pm, and drives him home. 

One day, Jack gets to the station an hour early, and starts walking home, until his wife meets him on the road. They get home 30 minutes earlier than usual. How long was he walking? 

Distances are unspecified. Speeds are unspecified, but constant.

Give a number which represents the answer in minutes.

He must be walking for....minutes. Click to know! 

Jack's Walking Duration in Journey!

What was the question?

It's important to think from wife's point of view in the case.

Ideally, had Jack somehow informed earlier his wife about his 1 hour early arrival then his wife's (and his as well) total 60 minutes in round trip would have been saved. 

30 minutes of her round trip are saved which means only 15 minutes of each leg of her trip must have been saved. That is she meets her husband only 15 minutes earlier on the day instead of 60 minutes earlier (if Jack had informed her earlier). 

Hence, Jack must be walking for 45 minutes.

Let's understand this with example.

Suppose wife needs exactly one hour to reach the station every day. She leaves home at 4 PM everyday and reach station at 5 PM & drive Jack home at 6 PM

On one day, Jack arrived at 4 PM and started walking whereas wife leaves home at the same time as usual. They reach home at 5:30 PM.

30 minutes of wife saved indicates that she took 45 minutes to meet husband (instead of 1 hour) at 4:45 PM (instead of 5PM, only 15 minutes earlier) and took him to home at 5:30 PM (instead of 6PM) in next 45 minutes (instead of 1 hour) thereby saving 15 + 15 = 30 minutes only.

Since, Jack started walking at 4 PM and meet her wife at 4:45 PM, he must be walking for 45 minutes.