Card puzzles

[red+black]

For those that didn't see me post these on another forum, have a go at solving these. They're quite do-able, so no cheating (ie. google):

Logic Puzzle #1

A maths professor asks his two brightest students, Fred and Tom, to his office to solve a logic puzzle. He says that there are 16 cards in his drawer:

Clubs: K, Q, 6, 5, 4
Diamonds: A, 5
Hearts: A, Q, 4
Spades: J, 8, 7, 4, 3, 2

The professor picks one card at random and tells the rank only to Fred, and the suit only to Tom. The professor asks them if they can each logically work out which card he picked. The students think about it for a while:

Fred: I don't know what the card is.
Tom: I know you don't know what the card is.
Fred: Oh, I know what the card is now.
Tom: Oh, I also know what the card is now.

Which card did the professor pick from his drawer?

Logic Puzzle #2

Using a standard English deck of cards, arrange an Ace, King, Queen and Jack in a single row across, using just one card of each suit:

1. The Spade is not adjacent to the Diamond
2. The suits alternate in colour
3. No card is adjacent to its next in rank
4. The King and Queen are facing each other (not necessarily adjacent though)
5. Both the King and the Jack sport a moustache

In order from left to right, what are the four cards?

[DoubleA]

*Removal of answer*

[red+black]

Gotta be the "something"......:cool:

I reiterate: For those that didn't see me post these on another forum

[DoubleA]

I reiterate: For those that didn't see me post these on another forum

...what do you mean :o

there I changed it now unquote me.

[Falchoon]

i never knew they faced different ways?

Kd- Jc- Ah- Qs
No moustaches on my set though?

http://david.bellot.free.fr/svg-cards/images/svg-cards-2.0.jpg

[Falchoon]

can't work oot the 1st one, but I'll go 4s.

[Falchoon]

1. 4s.

2. Kd- Jc- Ah- Qs

[red+black]

i never knew they faced different ways?

Kd- Jc- Ah- Qs
No moustaches on my set though?

http://david.bellot.free.fr/svg-cards/images/svg-cards-2.0.jpg

Using a standard English (http://en.wikipedia.org/wiki/Image:Set_of_playing_cards_52.JPG) deck of cards.

[Ricketts]

Clubs: K, Q, 6, 5, 4
Diamonds: A, 5
Hearts: A, Q, 4
Spades: J, 8, 7, 4, 3, 2

The professor picks one card at random and tells the rank only to Fred, and the suit only to Tom.

Well if he tells the rank to Fred, and Fred still doesn't know, that narrows it down to either an A,Q,5,4 as there are more than 1 of those.

Thats all from me. :)

[QueensofLeon]

4 Spades???

I think that is the answer I just can't really think of how to word it without sounding foolish.

[red+black]

4 Spades???

I think that is the answer I just can't really think of how to word it without sounding foolish.
I'm looking for logical reasoning and the mathematical proof. The process is more important than the end result.

[Falchoon]

btw my answers above are whited out,

here is my "process", also whited out

Clubs: K, Q, 6, 5, 4
Diamonds: A, 5
Hearts: A, Q, 4
Spades: J, 8, 7, 4, 3, 2


a k q j 10 9 8 7 6 5 4 3 2

Club k q 6 5 4
D a 5
h a q 4
s j 8 7 4 3 2


a k q j 10 9 8 7 6 5 4 3 2

Club q 5 4
D a 5
h a q 4
s 4

Fred: I don't know what the card is.
Tom: I know you don't know what the card is.
Fred: Oh, I know what the card is now.
Tom: Oh, I also know what the card is now.

Which card did the professor pick from his drawer?

odd one out gets the bikkies

[Falchoon]

Here's a tizzler for the poker board

Falchoon has 2 cars in his garage currently, (not counting the Mrs' go slow mobile).

One's an '86, one's an '05 both Aussie made. Name them ;)

[red+black]

Need. More. Clues.

[Falchoon]

Need. More. Clues.

I like to hoon ;)

[Binxy]

And here I was thinking you liked to falch.


Sorry, couldn't resist :p

[red+black]

For everyone's information, I am yet to see a single correct answer for either of the two puzzles I posted.

[red+black]

So, no takers huh?

[Falchoon]

So, no takers huh?

I'll have a go with the English deck over the weekend.




The answer to my question is ........ drumroll ........

1986 VL Commodore (the only car I've ever owned) & a
2005 VT Commodore

[red+black]

Two more puzzles:

Take all the Aces, Kings, Queens and Jacks from a deck so that you have just these 16 cards. Arrange them into a 4 x 4 matrix such that each row, column, and major diagonal contains only one card of each rank and suit.

Shouldn't take more than 5 minutes. Note that the answer is not unique.

============================================================

Take the 5s, 6s and 7s of Spades, Hearts and Diamonds from a deck so that you have just these 9 cards, and arrange them as such:

5s 6s 7s
7h 5h 6h
6d 7d 5d

The objective is to move the cards around such that each and every row, column and diagonal of your final matrix equals 18. What is the least number of card moves required to achieve this? Note that swapping the positions of two cards counts as 2 card moves, not 1.

[Borgsta]

The 2nd one is impossible. 21 is 7,7,7 so unless you can remove cards it is impossible.

[red+black]

The 2nd one is impossible. 21 is 7,7,7 so unless you can remove cards it is impossible.
Ha Ha :D I made a mistake. It should have read 18 (not 21). I've edited the puzzle.

[Borgsta]

Its still impossible with 9 cards to make something diagonally equal the same. At the moment every row and column equals 18 and 1 diagonal does too.

However you cant change them to equal 18 every diagonal way. To do that you'd need to have 1 card on the same row. ie.

5 6 5
7 6 5
7 6 7

Both diagonals now are 18 but the rows and columns are screwed.

[red+black]

Your solution to puzzle #1 is incorrect:

"such that each row, column, and major diagonal contains only one card of each rank and suit.

Puzzle #2 can be solved and it's easier than you would think. You need to not only show the final matrix, but to indicate how many moves it took.

[Borgsta]

Each suit. Oops can you tell Im a good reader. I'll edit it now.

I maintain its impossible if both diagonals must be met.

[red+black]

1st puzzle done. Properly this time.
Define "properly". For example, how many Aces of Spades in the average deck?

[Borgsta]

Define "properly". For example, how many Aces of Spades in the average deck?

Its a lot harder than you think without having a deck of cards here.

[Borgsta]

Diagonally yours doesnt equal 18.

[Falchoon]

Diagonally yours doesnt equal 18.

on further inspection I deleted it :cool:

[red+black]

OK, once and for all, while the final matrix is important, the main part of Puzzle #2 is

How many card moves are required?

[Borgsta]

Well if we arent worrying about the diagonal bit than zero moves are required. Every row and column already equals 18.

Is that correct?

[red+black]

Leading diagonal is actually 15 to begin with.

[jay_1972]

The answer to my question is ........ drumroll ........

1986 VL Commodore (the only car I've ever owned) & a
2005 VT Commodore
No idea with any of the card questions..but this statement is incorrect
2005 is VY or VZ
VT stopped in 01

[Borgsta]

Leading diagonal is actually 15 to begin with.

What does 'leading diagonal' mean? I guess its the one going from top left to bottom right. in that case, would it be


5s 6s 7s
6h 7h 5h
7d 5d 6d

with 6 moves. move every card across to the right on the 2nd row and every card 1 to the left on the 3rd.

[red+black]

Aaargh you're all stupid. I'll post the answers one day if I feel like it. Found an interesting problem:

You have been taken hostage, and your captors present you with a game for your life in a similar vein to Russian roulette. The game is holdem, and you are required to nominate cards as follows.

You must choose your opponent’s two hole cards, your own two hole cards, and three exposed flop cards. The simple situation is this. If you lose the hand at showdown, you will be killed. But you must choose cards that make you technically “behind” your opponent after the flop.

The challenge is to come up with the best mix of cards to maximise your chances of survival at showdown i.e. being behind, but with the greatest percentage chance of winning with two cards to come.

Logically there will be numerous combinations that provide the same percentage but I am curious to see the best combinations, and associated percentage chances of survival.

I’ve played around for a few minutes, and my best so far is 72.32% using the Odds Calculator on Card Player…

PS I would also be curious to know what you can come up with under the same scenario, but choosing cards that make you technically “behind” after the turn with only 1 card to come. Best I can do is 47.73%

OK, first combo that comes to mind for me is an OESFD with 2 overcards v a low pair, and according to twodimes, that is in fact the scenario mentioned above:

Holdem Hi: 990 enumerated boards containing Js Ts 8c
cards win %win lose %lose tie %tie EV
Ks Qs 716 72.32 274 27.68 0 0.00 0.723
2d 2h 274 27.68 716 72.32 0 0.00 0.277

Now the question is, can it get better than that?

[red+black]

Might as well get it out of the way now:

Logic Puzzle #1 solution
A maths professor asks his two brightest students, Fred and Tom, to his office to solve a logic puzzle. He says that there are 16 cards in his drawer:

Clubs: K, Q, 6, 5, 4
Diamonds: A, 5
Hearts: A, Q, 4
Spades: J, 8, 7, 4, 3, 2

The professor picks one card at random and tells the rank only to Fred, and the suit only to Tom. The professor asks them if they can each logically work out which card he picked. The students think about it for a while:

Fred: I don't know what the card is.
(knows the rank) Does not know the card as the rank is not unique. We now know card must be A, Q, 5 or 4.
Tom: I know you don't know what the card is.
(knows the suit) Does not know the card as each card in the known suit must be repeated in another suit. We now know card is a Diamond or a Heart.
Fred: Oh, I know what the card is now.
(knows the rank) Knowing what Tom knows, that the card is red (Diamond or Heart), it cannot be an Ace as he does not the suit. We now know the card must be 5d, Qh or 4h.
Tom: Oh, I also know what the card is now.
(knows the suit) Knows the card as there is just one remaining of that suit. Everyone now knows card must be 5d.

Logic Puzzle #2 solution
Using a standard English deck of cards, arrange an Ace, King, Queen and Jack in a single row across, using just one card of each suit:

1. The Spade is not adjacent to the Diamond.
S x D x
S x x D
x S x D
D x S x
D x x S
x D x S
2. The suits alternate in colour
S x x D or D x x S
ie. S H C D or D C H S
3. No card is adjacent to its next in rank
K J A Q or Q A J K
ie. Ks Jh Ac Qd or Kd Jc Ah Qs or Qs Ah Jc Kd or Qd Ac Jh Ks
4. The King and Queen are facing each other
Ks Jh Ac Qd or Qs Ah Jc Kd
5. Both the King and the Jack sport a moustache
Ks Jh Ac Qd

Logic Puzzle #3 solution
Take all the Aces, Kings, Queens and Jacks from a deck so that you have just these 16 cards. Arrange them into a 4 x 4 matrix such that each row, column, and major diagonal contains only one card of each rank and suit.

Shouldn't take more than 5 minutes. Note that the answer is not unique.

One possible solution:

As Kh Qd Jc
Qc Jd Ah Ks
Jh Qs Kc Ad
Kd Ac Js Qh

Logic Puzzle #4 solution
Take the 5s, 6s and 7s of Spades, Hearts and Diamonds from a deck so that you have just these 9 cards, and arrange them as such:

5s 6s 7s
7h 5h 6h
6d 7d 5d

The objective is to move the cards around such that each and every row, column and diagonal of your final matrix equals 18. What is the least number of card moves required to achieve this? Note that swapping the positions of two cards counts as 2 card moves, not 1.

Move # 1
6d
5s 6s 7s
7h 5h 6h
.... 7d 5d

Move #2
6d 7d
5s 6s 7s
7h 5h 6h
.... .... 5d

Move #3
6d 7d 5d
5s 6s 7s
7h 5h 6h

Answer: 3 card moves

[Ricketts]

Holdem game:

my cards: TsJs
opponent cards: 2d2h

flop: QsKs7c

[red+black]

Not quite as good:

pokenum -h js ts - 2d 2h -- qs ks 7c
Holdem Hi: 990 enumerated boards containing Ks Qs 7c
cards win %win lose %lose tie %tie EV
Js Ts 704 71.11 274 27.68 12 1.21 0.717
2d 2h 274 27.68 704 71.11 12 1.21 0.283