Srinivasa - The Nine of Spades
Srinivasa Ramanujan (1887-1920) is considered to be one the twentieth century's greatest mathematicians. While working as a clerk for the Madras Port Trust in 1912, he wrote to Professor G H Hardy of Cambridge University. In his letters he detailed a number of theorems, some of which Hardy identified as new and important.
So began a collaboration which would see Srinivasa publish no less than 26 mathematical papers in British journals and his election to the Royal Society of London. The Encyclopaedia Britannica says that he is recognised by mathematicians as a "phenomenal genius" without peer since Euler and Jacobi.
Numbers were Srinivasa's friends. Someone once remarked to him that a particular taxi number, 1729, was dull. Srinivasa immediately replied that "1729 is far from dull; indeed there is a certain class of numbers of which 1729 is the lowest". (Any guesses as to which class?)
The Pack's Srinivasa brought to the game the analytical skills of the genius he admired so much and the politeness of a person who plays bridge for its intellectual challenges. He carried that quiet air of someone who has learnt through the harshness of poverty and sickness what really matters in this life.
| Love All, Dealer East | Hypatia | ||
| ♠ Q84 | |||
| ♥ KQ876 | |||
| ♦ 9 | |||
| ♣ Q1054 | |||
| Hestia | Freud | ||
| Srinivasa | |||
| ♠ KJ93 | |||
| ♥ A | |||
| ♦ J1084 | |||
| ♣ AJ87 | |||
| West | North | East | South | |
| Hestia | Hypatia | Freud | Srinivasa | |
| 1♠1 | Pass | |||
| Pass | 2♥ | Pass | 3NT | |
| End | ||||
1. Five card major
Freud opened one spade, which promised a five card suit. Srinivasa toyed with an offbeat one no-trump but elected to pass and await developments. Hestia also passed and Hypatia protected with a two heart bid. Srinivasa considered for a moment - then closed the auction with a jump to three no-trump.
Hestia led the three of diamonds to east's queen. Freud cashed the king of diamonds and returned a diamond to Hestia's ace. On the fourth trick Hestia got off lead with a diamond on which Freud discarded a spade.
On the second, third and forth tricks dummy had discarded two hearts and a club to leave this position.
| Hypatia | |||
| ♠ Q84 | |||
| ♥ KQ8 | |||
| ♦ --- | |||
| ♣ Q105 | |||
| Srinivasa | |||
| ♠ KJ93 | |||
| ♥ A | |||
| ♦ --- | |||
| ♣ AJ87 | |||
Can you match the master's analysis before reading his thoughts?
Time to work on the numbers - but numbers are my forte. Since Hestia passed over Freud's opening bid I can be certain east holds the ace of spades and the king of clubs. He's also out of diamonds, so I should be able to make three hearts, two spades and three club tricks in addition to the diamond I already have.
The problem is - I can't be sure of reaching dummy to cash the hearts and take the club finesse. So what are my options? Well it's possible Freud holds the singleton king of clubs. If he has nine major suit cards, say six spades and three hearts or five spades and four hearts then he can only have one club.
Another chance is that west holds the singleton ten of spades. Then I can force an entry to dummy with the queen or the eight. If the ten fails to appear I can try for a singleton king of clubs.
Both these lines offer very poor odds. Is there anything better I wonder? Can I make the hand if east holds the two or more clubs and the ace and ten of spades?
Since I cannot play hearts or clubs, the play must be in the spade suit. If I play the king or jack, Freud will duck so logically I need to play a spade to the queen.
Yes that's it! Why didn't I see it sooner? If I play a spade to the queen after cashing the ace of hearts, Freud will be forced to win and return either a club, or a heart, or he will have to lead away from his ten of spades which I can let run to my eight. I'll need a card smaller than the eight in my hand so I will have to unblock the nine by playing it to the queen.
A quick recap just to be sure; I play the ace of hearts, followed by the nine of spades to the queen. If west holds the singleton ten of spades I can always reach dummy with the queen or eight. If east holds the ten of spades, which is much more likely, he'll be forced to provide an entry to dummy in one of the three suits.
East took the queen of spades and returned the suit. Srinivasa played low and as expected the eight took the trick. The hearts were cashed and the successful club finesse brought the contract home.
The full hand:
| Hypatia | |||
| ♠ Q84 | |||
| ♥ KQ876 | |||
| ♦ 9 | |||
| ♣ Q1054 | |||
| Hestia | Freud | ||
| ♠ 7 | ♠ A10652 | ||
| ♥ 9432 | ♥ J105 | ||
| ♦ A6532 | ♦ KQ7 | ||
| ♣ 632 | ♣ K9 | ||
| Srinivasa | |||
| ♠ KJ93 | |||
| ♥ A | |||
| ♦ J1084 | |||
| ♣ AJ87 | |||
Freud pointed out to Hestia that an initial spade lead, or a spade switch at trick four would have beaten the contract, but with the generosity that's the hallmark of his tribe, he was full of praise for Srinivasa's declarer play.
1729 is the lowest number which is the sum of two cubes in two different ways:
1 cubed plus 12 cubed = 1 + 1728 = 1729
10 cubed plus 9 cubed = 1000 + 729 = 1729