Sophie – The Eight of Spades
Sophie Germain 1776-1831, lived in Paris during France's revolutionary period. Not only did she have to cope with a country in turmoil but also with the belief of French academicians that mathematics was beyond the capabilities of the female mind. To get round the problem our heroine corresponded under the Nom de plume of "Monsieur LeBlanc". When circumstances forced her to reveal her identity to Carl Friedrich Gauss he replied in the following fashion.
A taste for the abstract sciences in general and above all the mysteries of numbers is excessively rare: the enchanting charms of this sublime science are revealed only to those who have the courage to go deeply into it. But when a person of the sex which, according to our customs and prejudices, must encounter infinitely more difficulties than men to familiarise herself with these thorny researches, succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of them, then without doubt she must have the noblest courage, quite extraordinary talents and superior genius.
Game All, Dealer East.
| Thoth | |||
| Putto | Santa | ||
| ♠ A1096 | |||
| ♥ 10983 | |||
| ♦ --- | |||
| ♣ AKQJ7 | |||
| Sophie | |||
| ♠ J853 | |||
| ♥ AKJ5 | |||
| ♦ K9 | |||
| ♣ 943 | |||
| West | North | East | South | |
| Putto | Thoth | Santa | Sophie | |
| 1♦ | Dbl | |||
| Rdbl | 1♥ | 1♠ | Pass | |
| 2♥1 | Pass | 3♦ | Pass | |
| 3♠ | Pass | 4♦2 | Pass | |
| 5♣2 | Pass | 5♥2 | Pass | |
| 6♠ | All Pass | |||
1. Game forcing
2. Control bids
Sophie led the ace of hearts and Putto, an habitual apologiser, confessed that he'd overbid as he thought they were playing with a thirty point pack, then blushed and apologised again as Santa followed with the four of hearts.
If you choose to take a minute or two to try to match Sophie's analysis and reasoning on this hand – be warned, you will find it a challenge to match her "extraordinary talents and superior genius".
Santa likes to keep the bidding simple when partnering Putto so most of their bids are easy to follow. It's curious that he didn't pass over Thoth's one heart. Obviously he considers his hand unsuitable for defence.
His cue bid and the four hearts in dummy makes it clear he started with a singleton. With five spades he would have rebid them over Putto's two heart inquiry – which leaves eight cards in the minors. He may be 5-3 in diamonds and clubs, but I don't imagine he would have cue bid in diamonds if he was looking at three club losers. No, it's more likely he's holding six or seven diamonds.
Now to points - twelve in hand, fourteen in dummy, twenty-six, leaving fourteen between North and East. Thoth has the queen of hearts so I expect Santa holds the remaining honour cards. If I'm right the hand has become double dummy problem with twelve cards left.
| Thoth | |||
| ♠ x | |||
| ♥ Qxx | |||
| ♦ xxxxx | |||
| ♣ xxx | |||
| Putto | Santa | ||
| ♠ A1096 | ♠ KQxx | ||
| ♥ 1098 | ♥ --- | ||
| ♦ --- | ♦ AQxxxx | ||
| ♣ AKQJ7 | ♣ xx | ||
| Sophie | |||
| ♠ J853 | |||
| ♥ KJ5 | |||
| ♦ K9 | |||
| ♣ 943 | |||
Santa has a remarkable skill for hand reading, and if I can picture his hand, it's equally certain he can picture mine. Doubtless he'll deduce hearts are 4-4, he'll know I've the king of diamonds and that I'm likely to hold four spades for my double.
Counting tricks – declarer has five club winners, the ace of diamonds and four spades, two short of the twelve he needs. He might try to establish his diamond suit. Can he do that without shortening his trumps? Let's see, for that he'll need an entry to his hand to play diamonds, another entry to finesse my jack of spades and a third entry to draw trumps and cash the diamonds. The king and queen of trumps provide two entries to his hand but fortunately for us the third is lacking.
An alternative for declarer is to ruff two hearts, but that will leave him with KQ opposite AT96 in spades, in which case he won't make unless he can arrange some sort of trump coup. I'd better play it through to see if danger lies in that direction.
Say I play a second heart, declarer ruffs, ace and a diamond ruff follow. Santa knows the side suits should be cashed to execute the coup so he'll play three rounds of clubs before ruffing a second heart. That leaves us with five cards each and East on lead.
| Thoth | |||
| ♠ x | |||
| ♥ Q | |||
| ♦ xxx | |||
| ♣ --- | |||
| Putto | Santa | ||
| ♠ A109 | ♠ KQ | ||
| ♥ --- | ♥ --- | ||
| ♦ --- | ♦ Qxx | ||
| ♣ J7 | ♣ --- | ||
| Sophie | |||
| ♠ J853 | |||
| ♥ J | |||
| ♦ --- | |||
| ♣ --- | |||
That's annoying – Santa can crossruff the last five tricks to make his contract. Effectively he makes three club tricks, one diamond and eight trumps to score his contract.
A club at trick two leads to an identical position and a diamond round to the ace-queen is equivalent to waving a white flag, which leaves a trump switch. The jack of spades gives declarer an easy twelve tricks; four spades, two heart ruffs, one diamond and five clubs.
So I've eliminated every option except a small spade. Say I switch to a trump at trick two? We'll reach the same end position except everyone will have a spade less. Santa can crossruff three of the four tricks with dummy's A10 and his king, but the final trick will be mine! In effect the trump lead cuts declarer's spade winners from eight to seven.
So that's the solution, I'll lead a spade and Santa has no counter move…
Except, mon dieu! What if he's able to win the first trick with the seven? I reasoned earlier the contract will make if declarer can find three trump entries to his hand. After ruffing a diamond in dummy my trumps will fall under the ace, king and queen and Santa can claim his contract.
The solution is as obvious as a fourth-order partial differential equation; I need to play my name card, that's the Eight of Spades. Santa will be forced to take this trick in dummy with the nine or in his hand with the queen. Either way, in the endgame, I'll make a second trick and defeat the contract.
The full deal:
| Thoth | |||
| ♠ 2 | |||
| ♥ Q762 | |||
| ♦ 108542 | |||
| ♣ 1062 | |||
| Putto | Santa | ||
| ♠ A1096 | ♠ KQ74 | ||
| ♥ 10983 | ♥ 4 | ||
| ♦ --- | ♦ AQJ763 | ||
| ♣ AKQJ7 | ♣ 85 | ||
| Sophie | |||
| ♠ J853 | |||
| ♥ AKJ5 | |||
| ♦ K9 | |||
| ♣ 943 | |||
When Socrates and Sophie discussed the hand after the session they agreed the eight of spades beats the contract if west has five or more diamonds. When he asked Sophie what led her to the solution she remarked… "If you recall, the other spades in my hand were the Jack, Five and Three – otherwise know as Aristotle, Alan and Charles, and as you know, there's an old bridge saw that says… you should never send a boy on a woman's errand."
When Gustave Eiffel built his famous tower he incorporated 72 plaques listing the names of prominent French scientists and mathematicians. One name that's conspicuous by it absence is Sophie's, which is surprising as she formulated the techniques that were used to calculate the stress in its beams during the tower's design.
Our heroine is commemorated in mathematics by "Sophie Germain Primes". These are defined as a prime p which generates a second prime when it is doubled and increased by one, 2p + 1. For example, 11 qualifies as 2p+1 = 23, 17 is excluded as 2p+1 equals 35 – a non-prime. Readers with a little time to spare might like to confirm that 648,621,027,630,345 × 2253824-1 is a Sophie Germain Prime.
Mike Chanter
This sequence of articles was written and conceived by Mike Chanter.
Mike has been a member of Suffolk for a long time despite no longer living in the county and retaining his connection by being an associate. He still has many friends in Suffolk and returns from time to time to play in local events. He would be delighted to hear your impressions of Bridge in the Cupboard.