Card game

Logic Level 2

You are playing a game with your friend.

It is played with a deck of only 16 cards, divided into 4 suits: Red , Blue , Orange \color{#D61F06} \text{Red}, \color{#3D99F6}\text{Blue}, \color{#EC7300} \text{Orange} and Green . \color{#20A900} \text{Green}.

There are four cards in each suit: Ace, King, Queen and Jack.

Ace outranks King, which outranks Queen, which outranks Jack - except for the Green \color{#20A900} \text{Green} Jack, which outranks every other card.

If two cards have the same face value, then Red \color{#D61F06} \text{Red} outranks Blue \color{#3D99F6} \text{Blue} , which outranks Orange \color{#EC7300}\text{Orange} , which outranks Green \color{#20A900}\text{Green} , again except for the Green \color{#20A900} \text{Green} Jack, which outranks everything.

Here's how the game is played:

You are dealt one card face up, and your friend is dealt one card face down. Your friend then makes some true statements, and you have to work out who has the higher card, you or your friend. It's that simple!

You are dealt the Blue \color{#3D99F6}\text{Blue} King and your friend makes three statements:

  • Statement 1:. My card would beat a Green \color{#20A900} \text{Green} King.

  • Statement 2: Knowing this, if my card is more likely to be a Jack than a Queen, then my card is a King. Otherwise, it isn't.

  • Statement 3. Given all of the information you now know, if my card is more likely to beat yours than not, then my card is Red \color{#D61F06} \text{Red} card. Otherwise, it isn't.

Who has the higher card?

Neither You Your friend

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Stephen Brown
Nov 28, 2017

Statement 1 narrows your friend down to a non-Green King, an Ace, or a Green Jack. Thus there's a 1/8 chance the card is a Jack and 0 chance it's a Queen. Statement 2 reveals that the card is a King. Since you have the Blue King, your friend must have either the Red King or the Orange King. There's an equal chance of your friend's card being better or worse than your own; that is, it is NOT more likely to beat yours than not. Your friend tells you this means the card is not Red, so your friend must have the Orange King, and your Blue King is higher.

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...