## Puzzles

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### Re: Puzzles

questionable_i wrote:5 Pirates Puzzle

5 pirates of different ages have a treasure of 100 gold coins.

On their ship, they decide to split the coins using this scheme:

The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it.

If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain.

As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard.

Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen?

My guess would be there would be :

Round 1. Whatever the oldest pirate suggest, the other 4 will vote against. 4 - 1 Oldest pirate dies!

Round 2. Whatever Pirate2 suggest, the other 3 will vote against. 3 - 1 Pirate2 dies!

Round 3. Pirate3 should suggest Pirate4 gets 33coins, Pirate5 gets 34coins and himself gets 33coins. Pirate5 says AYE! Pirate4 says NO! Pirate3 says AYE! Since he won't wanna die.

icy_mama
KiasuGrandMaster

Posts: 11026
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### Re: Puzzles

icy_mama wrote:
questionable_i wrote:5 Pirates Puzzle

5 pirates of different ages have a treasure of 100 gold coins.

On their ship, they decide to split the coins using this scheme:

The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it.

If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain.

As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard.

Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen?

My guess would be there would be :

Round 1. Whatever the oldest pirate suggest, the other 4 will vote against. 4 - 1 Oldest pirate dies!

Round 2. Whatever Pirate2 suggest, the other 3 will vote against. 3 - 1 Pirate2 dies!

Round 3. Pirate3 should suggest Pirate4 gets 33coins, Pirate5 gets 34coins and himself gets 33coins. Pirate5 says AYE! Pirate4 says NO! Pirate3 says AYE! Since he won't wanna die.

The answer is something like that:

The oldest pirate will propose a 98 : 0 : 1 : 0 : 1 split, in other words the oldest pirate gets 98 coins, the middle pirate gets 1 coin and the youngest gets 1 coin.

Let us name the pirates (from oldest to youngest): Alex, Billy, Colin, Duncan and Eddie.

Working backwards:

2 Pirates: Duncan splits the coins 100 : 0 (giving himself all the gold). His vote (50%) is enough to ensure the deal.

3 Pirates: Colin splits the coins 99 : 0 : 1. Eddie will accept this deal (getting just 1 coin), because he knows that if he rejects the deal there will be only two pirates left, and he gets nothing.

4 Pirates: Billy splits the coins 99 : 0 : 1 : 0. By the same reasoning as before, Duncan will support this deal. Billy would not waste a spare coin on Colin, because Colin knows that if he rejects the proposal, he will pocket 99 coins once Billy is thrown overboard. Billy would also not give a coin to Eddie, because Eddie knows that if he rejects the proposal, he will receive a coin from Colin in the next round anyway.

5 Pirates: Alex splits the coins 98 : 0 : 1 : 0 : 1. By offering a gold coin to Colin (who would otherwise get nothing) he is assured of a deal.

(Note: In the final deal Alex would not give a coin to Billy, who knows he can pocket 99 coins if he votes against Alex's proposal and Alex goes overboard. Likewise, Alex would not give a coin to Duncan, because Duncan knows that if he votes against the proposal, Alex will be voted overboard and Billy will propose to offer Duncan the same single coin as Alex. All else equal, Duncan would rather see Alex go overboard and collect his one coin from Billy.)

questionable_i
BrownBelt

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### Re: Puzzles

that's some mind moggling mind games!

good one, Q_i! keep it coming!

icy_mama
KiasuGrandMaster

Posts: 11026
Joined: Sat Apr 27, 2013 2:24 pm
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### Re: Puzzles

Hi, there, this is a new puzzles for you guys to solve:

Two old friends, Jack and Bill, meet after a long time.

Three kids
Jack: Hey, how are you man?
Bill: Not bad, got married and I have three kids now.
Jack: That’s awesome. How old are they?
Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Jack: Cool… But I still don’t know.
Bill: My eldest kid just started taking piano lessons.
Jack: Oh now I get it.

How old are Bill’s kids?

questionable_i
BrownBelt

Posts: 526
Joined: Sat Oct 10, 2015 5:39 pm
Total Likes: 1

### Re: Puzzles

questionable_i wrote:Hi, there, this is a new puzzles for you guys to solve:

Two old friends, Jack and Bill, meet after a long time.

Three kids
Jack: Hey, how are you man?
Bill: Not bad, got married and I have three kids now.
Jack: That’s awesome. How old are they?
Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Jack: Cool… But I still don’t know.
Bill: My eldest kid just started taking piano lessons.
Jack: Oh now I get it.

How old are Bill’s kids?

Product of 3 numbers -- (sum of the 3 numbers in brackets) that equals 72 :
1. 1, 1, 72 -- (74)
2. 1, 2, 36 -- (39)
3. 1, 3, 24 -- (28)
4. 1, 4, 18 -- (23)
5. 1, 6, 12 -- (19)
6. 1, 8, 9 -- (18)
7. 2, 2, 18 –- (22)
8. 2, 4, 9 – (15)
9. 2, 6, 6 – (14)
10. 2, 3, 12 – (17)
11. 3, 4, 6 – (13)
12. 3, 3, 8 – (14)

1. The sum must be 14 as both the sum and product of the ages did not give Jack enough information.
2. The word 'eldest' eliminates 9. with 12. left as the solution.

Ans : 3, 3, 8.

alfretztay
KiasuGrandMaster

Posts: 1269
Joined: Sun Sep 12, 2010 11:56 am
Total Likes: 5

### Re: Puzzles

alfretztay wrote:
questionable_i wrote:Hi, there, this is a new puzzles for you guys to solve:

Two old friends, Jack and Bill, meet after a long time.

Three kids
Jack: Hey, how are you man?
Bill: Not bad, got married and I have three kids now.
Jack: That’s awesome. How old are they?
Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Jack: Cool… But I still don’t know.
Bill: My eldest kid just started taking piano lessons.
Jack: Oh now I get it.

How old are Bill’s kids?

Product of 3 numbers -- (sum of the 3 numbers in brackets) that equals 72 :
1. 1, 1, 72 -- (74)
2. 1, 2, 36 -- (39)
3. 1, 3, 24 -- (28)
4. 1, 4, 18 -- (23)
5. 1, 6, 12 -- (19)
6. 1, 8, 9 -- (18)
7. 2, 2, 18 –- (22)
8. 2, 4, 9 – (15)
9. 2, 6, 6 – (14)
10. 2, 3, 12 – (17)
11. 3, 4, 6 – (13)
12. 3, 3, 8 – (14)

1. The sum must be 14 as both the sum and product of the ages did not give Jack enough information.
2. The word 'eldest' eliminates 9. with 12. left as the solution.

Ans : 3, 3, 8.

You're correct. Bingo!

questionable_i
BrownBelt

Posts: 526
Joined: Sat Oct 10, 2015 5:39 pm
Total Likes: 1

### Re: Puzzles

questionable_i wrote:
alfretztay wrote:
questionable_i wrote:Hi, there, this is a new puzzles for you guys to solve:

Two old friends, Jack and Bill, meet after a long time.

Three kids
Jack: Hey, how are you man?
Bill: Not bad, got married and I have three kids now.
Jack: That’s awesome. How old are they?
Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Jack: Cool… But I still don’t know.
Bill: My eldest kid just started taking piano lessons.
Jack: Oh now I get it.

How old are Bill’s kids?

Product of 3 numbers -- (sum of the 3 numbers in brackets) that equals 72 :
1. 1, 1, 72 -- (74)
2. 1, 2, 36 -- (39)
3. 1, 3, 24 -- (28)
4. 1, 4, 18 -- (23)
5. 1, 6, 12 -- (19)
6. 1, 8, 9 -- (18)
7. 2, 2, 18 –- (22)
8. 2, 4, 9 – (15)
9. 2, 6, 6 – (14)
10. 2, 3, 12 – (17)
11. 3, 4, 6 – (13)
12. 3, 3, 8 – (14)

1. The sum must be 14 as both the sum and product of the ages did not give Jack enough information.
2. The word 'eldest' eliminates 9. with 12. left as the solution.

Ans : 3, 3, 8.

You're correct. Bingo!

Thank you!

One for all who visit this thread : 9 – 3 ÷ 1/3 + 1 =?

alfretztay
KiasuGrandMaster

Posts: 1269
Joined: Sun Sep 12, 2010 11:56 am
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### Re: Puzzles

As it has not been answered, from previous post, question 1 : "one for all who visit this thread : 9 – 3 ÷ 1/3 + 1 =?"

Q2.
8 @ 2 = 16106
5 @ 4 = 2091
9 @ 6 = 54153
7 @ 5 = 35122
20 @ 3 = 602317
8 @ 3 = ?

Q3.
(a) 6 / 2(1 + 2) = ?
(b) 6/2(1 + 2) = ?

alfretztay
KiasuGrandMaster

Posts: 1269
Joined: Sun Sep 12, 2010 11:56 am
Total Likes: 5

### Re: Puzzles

I love the puzzles! Thanks for sharing

Chloetanscgs
YellowBelt

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