Puzzle 8Q63 Main

Suitable Accounting

by Richard Pavlicek

There are exactly 8192 (2¹³) possible suit holdings, from a void to AKQJT98765432. Surely you’ve held the majority of them, and probably all of the shorter lengths. For the extreme lengths, frequency drops fast, though most players have held a 9-card suit, some have held 10, and a lucky few 11. I am unaware of a 12-card suit, let alone 13, ever occurring in an official event, but they abound in fantasy problems and puzzles (for which I plead the Fifth). For more on the topic see Long Suit Story, but don’t let that interfere with your accounting job here.

Are you a suitable accountant? Test yourself or make your best guesses, but have no fear. You won’t be held accountable! Consider the following six categories, and which suit holdings fit in each. For example, K83 would fit in every category except #4.

Assume every suit holding is in card-rank order (using T for 10) as in this Data File.

How many of the 8192 suit holdings fit in each category?

1. Odd number of cards

2. More odd ranks (KJ9753) than even

3. Exactly 3 high-card points

4. At least one straight flush

5. No adjacent card ranks

6. Digit string a prime number

Puzzle 8Q63 Main Top Suitable Accounting

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Puzzle 8Q63 Main Top Suitable Accounting