Main   Puzzle 8S99 by Richard Pavlicek  

October Octillions

Some things are difficult to comprehend, like the Einstein Cross Quasar (pictured above) 8 billion light-years from Earth, or the staggering number of bridge deals — or even partner making the right lead against 3 NT. While pondering that, suppose you are East on this deal that decided the Sector 9 championship of Owl Nebula (pictured right) only 2600 light-years away:

Board 1.948329 E+28 S 10 8 7
H K 7 2
D K 6 5 3 2
C J 8
E-W Vul   Partner


3 NT
2 S
2 NT
H J 9
D Q J 10 9 8 7
C K 10 9 4
Table S A Q 5 4 3 2
H Q 10 8
C 7 6 3 2
3 NT South S K 9 6
H A 6 5 4 3
D A 4
C A Q 5

With an empty suit at adverse vulnerability (redshift +1.0127) opening 2 S was nebulous, but then so was the atmosphere. South lands in 3 NT, and partner of course leads a diamond — arguably your fault for not opening 2 D (then partner would have led a spade). You discard a spade, South wins the D A and leads three rounds of hearts to your queen. Game over. If you lead a club, declarer ducks; if a low spade, he hops. Either way declarer is destined for nine tricks: one spade, four hearts, two diamonds and two clubs.

The defense to beat 3 NT is cute: West must lead the S J, which East and South duck. Partner got one lead right, but will he get another? No, the straight flush (two in fact) in diamonds is too tempting. Only a club shift will foil declarer, allowing the defense to establish two club tricks, besides a heart and two spades, before declarer can develop nine.

An interesting deal but hardly spectacular, and a bit humbling when you consider that it’s only one out of octillions. North-South have a 5-3 heart fit but wouldn’t enjoy 4 H; down three as the defense crossruffs early and scores the C K later. North-South also have a 5-2 fit in diamonds — don’t play there — nor would East-West enjoy their 4-4 fit in clubs or 6-1 in spades. Aggregately, each side has one 8-card fit and one 7-card fit. The best East-West can do is to win seven tricks in spades, so the par contract is 2 NT North-South (plus 120).

Other notable (or not) features are the individual suit lengths: five 3-card suits (most common by far), three doubletons, two each of 4-6 lengths, one singleton and one void. Not surprisingly, half of these are odd length, and half are even length. How many straight flushes do you see? The answer is three, which is high for a deal. Besides West having two in diamonds, East has a subtle one in spades (the ace can be low in poker). The deal also contains 17 touching cards (as defined in Parity Clarity).

Haunting perspectives:  The number of unique bridge deals is 53.6 octillion (29 digits).
Astrophysicists estimate all life on Earth will end in 31.5 quadrillion seconds (17 digits).
Organizational incompetence indicates bridge will end in 2.4 billion seconds (10 digits).

Trying to comprehend all this, you take an evening walk. Looking skyward to the constellation Taurus, you spot the bright orange star Aldebaran (pictured right) — a relative neighbor only 65 light-years away. But alas, it is still too overwhelming. You could visit Aldebaran, the Nebula and the Quasar a thousand times (call Elon Musk for tickets) before you could witness every bridge deal. Don’t even think about it! But wait! You will have to think about it to participate in this puzzle contest.

Challenge yourself with this octet of octillions — or make your best guesses!

  In all 53,644,737,765,488,792,839,237,440,000 bridge deals, which is greater?
1. Number of odd-length suits or Number of even-length suitsEqual
2. Number of 5-3 fitsor Number of 5-2 fitsEqual
3. Number of 6-4 fitsor Number of straight flushesEqual
4. Number of 7-card fitsor Number of 6-card fitsEqual
5. Number of void suitsor Number of hands with 3-4 acesEqual
6. Number of 5-5 fitsor Inches to Einstein Cross Quasar*
7. Number of 3-card suitsor Angstroms to Owl Nebula*
8. Number of touching cardsor Picometers to Aldebaran*

*Assume distances given on this page are exact for comparison purposes.

Answers may be submitted until Halloween (October 31) midnight GMT — multiple times if you wish, but only the latest one counts. Correct answers and a list of top solvers will be published here on November 1. Are you feeling lucky?

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© 2021 Richard Pavlicek