Story of Distiribution of 100 Coins Loot

Five ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain).

The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go “Aye”, the loot is divided as proposed, as no pirate would be willing to take on the captain without superior force on their side.

If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him walk the plank. The pirates start over again with the next senior pirate as captain.

What is the maximum number of coins the captain can keep without risking his life?

He can take away 98 coins! How? Read here! 

The Captain's Undeniable Proposal

What was the situation?  

He can keep 98 coins! Surprised? Read how.

Let's number 5 pirates as Pirate 5, Pirate 4.....Pirate 1 as per their descending order of seniority.

Pirate 5 keeps 98 coins with him and gives 1 coin each to Pirate 3 and Pirate 1.

Now Pirate 5 i.e Captain explains his decision -

CASE 1:

 If there were only 2 pirates then Pirate 2 would have taken all 100 coins after obtaining his own vote which accounts to 50% votes (50 % of 2 = 1).

CASE 2: 

 In case of 3 pirates, the Pirate 3 would have offered 1 coin to Pirate 1 & would have kept 99 coins with him. Now Pirate 1 wouldn't have any option other than agreeing on deal with Pirate 3. That's because if he doesn't agree then Pirate 3 would be eliminated & all coins would be with Pirate 2 as explained in above (case 1) of only 2 pirates. So votes of Pirate 1 and Pirate 3 which account to 66% (2 out of 3) votes of group locks this deal and Pirate 2 would be left without any coin.

CASE 3: 

 Now in case of 4 pirates, Pirate 4 would offer coin to Pirate 2 & would keep 99 coins with him. Now, Pirate 2 know what happens if Pirate 4 gets eliminated. Pirate 3 would offer 1 coin to Pirate 1 & will take away 99 coins. So Pirate 2 would definitely accept this deal. That's how votes of Pirate 4 and Pirate 2 makes 50% (2 out of 4) votes of group to pass the proposal. Pirate 3 and Pirate 1 can't do anything in this case.

By now, Pirate 3 and Pirate 1 realizes what happens of Pirate 5 gets eliminated. They won't be getting any coin if Pirate 4 becomes captain as explained above (case 3). So they have no option other than to vote for the proposal of Pirate 5. 

This way, Pirate 5, Pirate 3 and Pirate 1 (3/5 = 60% of crew) agree on proposal of Pirate 5 where he takes away 98 coins with 1 coin each to Pirate 3 and Pirate 1. 

'Morning Melange' - Puzzle

This morning, the popular Bay area cable access TV show, "Morning Melange", featured six guests (including Francine and Evan). Each guest lives in a different town in the region (including Corte Madera), and each has a different talent or interest that was the focus of his or her segment. The segments began at 6:45, 7:00, 7:15, 7:30, 7:45 and 8:00. 

Discover, for each time, the full name of the featured guest, where he or she lives and his or her special interest.
 
1. The first three guests were, in some order: the person surnamed Ivens, the person from Berkeley and the antique car collector.

2. Damien's segment was sometime before Lautremont's segment.

3. Krieger's segment began at 7:45.

4. Alice appeared after the person from Oakland and before the person surnamed Morley.

5. The people from Berkeley and Daly City aren't of the same sex.

6. The six guests were: Cathy, the person whose first name is Damien, the person whose last name is Novak, the person from Daly City, the person from Palo Alto and the bungee jumper.

7. The last name of the financial adviser is either Lautremont or Novak.

8. Jaspersen's segment began exactly 45 minutes after the beekeeper's segment.

9. The crepe chef went on sometime before the person from Sausalito and sometime after Brandon.

10. The hypnotherapist's segment began at 7:15.

HERE is SOLUTION! 

'Morning Melgane' Puzzle - Solution

What was the puzzle?

Rewriting all the given clues once again.

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1. The first three guests were, in some order: the person surnamed Ivens, the person from Berkeley and the antique car collector.

2. Damien's segment was sometime before Lautremont's segment.

3. Krieger's segment began at 7:45.

4. Alice appeared after the person from Oakland and before the person surnamed Morley.

5. The people from Berkeley and Daly City aren't of the same sex.

6. The six guests were: Cathy, the person whose first name is Damien, the person whose last name is Novak, the person from Daly City, the person from Palo Alto and the bungee jumper.

7. The last name of the financial adviser is either Lautremont or Novak.

8. Jaspersen's segment began exactly 45 minutes after the beekeeper's segment.

9. The crepe chef went on sometime before the person from Sausalito and sometime after Brandon.

10. The hypnotherapist's segment began at 7:15.

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STEPS :

1] Let's make table like below for simplicity & easy understanding.

   
2] As per (10), hypnotherapist took segment starting at 7:15 & (3) suggest that Krieger started at 7:45.

3] As per (8), Jaspersen must be either at 7:30, 7:45 or 8:00 (i.e. in second half) while beekeeper must be at 6:45 or 7:00 or 7:15. But 7:15 segment is already occupied by hypnotherapist and Krieger is there already at 7:45.
So, Jaspersen can't be at 7:45. Hence, Jaspersen must be at 7:30 and beekeeper at 6:15 for (8) to be true.

With that, the antique car collector pointed by (1) must be at 6:45.

4] Since, as per (7), the financial adviser isn't Jaspersen or Kreiger ,therefore is on during the 8:00 segment. As per (4), Morley can't be in first 2 segments & as per (7) Morely is not a financial adviser. Thus, Morley needs to be at 7:15.

5] With that as (4) suggests, Alice must be on during segment started at 7:00 & person from Oakland took 6:45.

6] Now, as (1) suggests person having surname Ivans has to be at 6:45 & the person at Berkeley must be at 7:15.

7] The two guests appeared in the 6:45 and 7:15 segments can't be Novak, from Daly City or Palo Alto, or interested in bungee jumping (Hint 6). Therefore, these guests must be Cathy and Damien.

8] So for (9) to be Brandon must be at 7:30,  the chef must be at 7:45, and the guest from Sausalito at 8:00.

9] There are 6 different guest pointed by Hint (6). So, the bungee jumper who has to at 7:30 can't be from Daly City or Palo Alto. Hence, he must be from Corte Madera. 

10] Now, Alice has to be from Daly City or Palo Alto & hence can't have surname Novak as (6) points 6 different guests. Therefore, Novak must be at 8:00 and Alice at 7:00 must be Lautremont.

 11] With that, the hint (2) suggests that Damien must be at 6:45 and hence Cathy at 7:15.

12] Now it's clear that, Cathy is from Berkeley & hence as (5) suggests Alice can't be from Dale City and is therefore from Palo Alto. So Krieger must be from Dale City.

13] In the last, as per (5) itself, Kreiger, who is from Daly City, cannot be Francine, and must be named Evan. This leaves Francine at 8:00. 

 

A Man Walking on Railroad Bridge

A man is walking across a railroad bridge that goes from point A to point B. He starts at point A, and when he is 3/8 of the way across the bridge, he hears a train approaching. The train's speed is 60 mph (miles per hour). The man can run fast enough so that if he turns and runs back toward point A, he will meet the train at A, and if he runs forward toward point B, the train will overtake him at B.

How fast can the man run?


He must be running at 'this' speed! 

Speed Needed For Run on Bridge

Why to calculate the speed?

If the man turns back and runs towards A for 3/8 of distance while train reaches at the point A. That means the train train reaches at point A when man runs for 3/8 distance.

So if man continues to run towards point B then, while he covers 3/8 distance the train reaches at point A. Now, man is 3/8 + 3/8 = 6/8 = 3/4 distance away from the point A where B is 1/4 away from him now.

Again, we know, the train will overtake the man at point B covering total distance between A and B. Till then man can run only 1/4 th distance between A and B to reach B.That mean the train must be 4 times faster than the speed of man.

Since, train is traveling at 60 mph, the speed of man = (1/4)x60 = 15 mph.

The Case of Fourth Mystery Number

There is a ten-digit mystery number (no leading 0), represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once. 

Given the following clues, what is the number?

1) B + C + F + J = E + G + H + I = AD
2) B - H = J - G = 3
3) C - F = E - I = 5
4) B * I = AJ

Here are steps demystifying the mystery number! 

The First Case of Mystery Number 

The Second Case of Mystery Number 

The Third Case of Mystery Number