SOLUTION TO A LOGIC PROBLEM BY ENUMERATION

PROBLEM:

A playing card hand contains:

  1. Exactly 13 cards
  2. At least one card from each suit
  3. A different number of cards in each suit
  4. A total of 5 cards from "hearts" and "diamonds"
  5. A total of 6 cards from "diamonds" and "spades"
  6. Exactly 2 trump cards

What is the trump suit?

WHAT DO WE KNOW?

  • There are four suits in a deck of playing cards - hearts, clubs, diamonds, and spades
  • The "trump" suit can be any suit in the deck
  • The face values of the cards are irrelevant

SOLUTION:

Gross method:

Write down all the possible combinations of cards and check whether the combination of numbers of cards meets the requirements:

Hearts
Clubs
Diamonds
Spades
1
1
1
10
2
1
1
9
3
1
1
8
4
1
1
7
5
1
1
6
6
1
1
5
7
1
1
4
8
1
1
3
9
1
1
2
10
1
1
1
1
1
1
10
1
2
1
9
2
2
1
8
3
2
1
7

 

and so on

How many cases do we have to consider?

Or, how many ways are there that four numbers can add up to 13?

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Last updated 2000/01/21
© J.A.N. Lee, 2000.