New Haven/ Winston Salem
New Haven/ Winston Salem
TODAY’S MEN’S NEWS
Winston-Salem
Singles – Quarterfinal: (6) S Querrey def. R Berankis 6-3 6-4
At least there is one seed around here who wants to win. Sam Querrey defends his points, and while that doesn’t assure that he will stay Top Thirty, his chances look good.
Singles – Quarterfinal: (15) G Monfils def. (7) F Verdasco 6-7(8-10) 6-4 6-4
Is there some law that says higher seeds (other than Querrey) cannot win around here? Fernando Verdasco made it seven of eight high seeds to go out to lower players or injury. He stays around #30; Gael Monfils is one win away from the Top Forty.
Singles – Quarterfinal: (9) J Melzer def. (13) D Tursunov 6-4 6-3
Could Jurgen Melzer be coming back to life? He’s getting close to the Top Thirty. Although he seemed jinxed; rain stopped this match one game from the end.
Singles – Quarterfinal: (10) A Dolgopolov def. Y Lu 7-6(7-2) 6-3
This still doesn’t represent much of a move for Alexandr Dolgopolov, but if he can make the final, he’ll rise to around #35.
TODAY’S FEATURE
Doublets Specialist
This year marked the hundred and fiftieth anniversary of the split between Charles Dodgson (Lewis Carroll) and the Liddell family. Not exactly something to celebrate — it put Dodgson into at least an eight year bout of depression — but we thought we’d celebrate some of his works.
Besides, it will give you something to do during those U. S. Open rain delays. Or maybe give Jimmy Connors a way to pass the time while he waits for a phone call.
One of the many games invented by Lewis Carroll was something he called “Doublets.” The idea is to take two words of the same length and convert one to the other by changing only one letter at a time. A constraint is that every intermediate stage must be a word in its own right. For example, GRASS can be made GREEN as follows:
GRASS
CRASS
CRESS
TRESS
TREES
TREED
GREED
GREEN
This is a seven-step transformation. It is of course obvious that the minimum transformation for two words is the number of letters which are different. For example, SOD and SAT differ by two letters, and can be converted in a two-step transformation:
SOD
SOT
SAT
or
SOD
SAD
SAT
(This shows that there are often multiple ways to get from one word to another.)
Some transformations take more steps than just the number of differences.. For example, OLD and OAT differ by two letters, but you cannot get from one to the other in two steps, because there are only two possible intermediate stages (OLT and OAD), and neither is a word. It is possible to get from one to the other, but it’s a long path — the only word that is one letter away from OLD is ODD (and the only other word one letter away from ODD is ADD), and the only words one letter away from OAT that keep the initial O are OAF, OAK, OAR, OFT, OPT, and OUT. The shortest route we could find (and we used a spreadsheet to do the hunt, although even that doesn’t guarantee that we found the shortest path) is
OLD
ODD
ADD
AND
ANT
AFT
OFT
OAT
Some transformations are not possible at all. This is more typically true of very long words; there just aren’t enough one-letter-away words to operate with. But it can happen with short words, too, especially if they involve rare letters like Q or Z. Any doublet for QUIZ, e.g., has to start through QUIT or QUIP (or, if you’re British, QUID).
The ideal transform is considered to be the shortest possible.
Having read about this game in one of Martin Gardner’s old Mathematical Recreations columns, we decided to work up some tennis doublets. We have run many of these before, but this is good practice for the second game we have in mind.
As a very simple start, trying making a HIT go OUT in two steps.
Lewis Carroll himself proposed one that would have fit well with some of this year’s events: Turn WET into DRY in no more than five steps.
A BALL can get you to a GAME in at least two ways that are three steps long.
It takes just three steps to cross the BASE LINE.
You can get a LINE CALL in five steps.
You can get players to move from CLAY to HARD if you use a GOAD along the way, but it takes seven steps.
A player with lots of SLICE can produce many SPINS.
You can make CORD into NETS in five steps.
If you don’t hit a LET, you might hit an ACE, and that might win you a SET. There are no more than seven steps along the way.
If you’re Serena Williams, a CURSE can turn into FINES in six steps if you allow PONES (as in corn pone) along the way, perhaps seven otherwise.
A tennis-specific variation would be to allow players’ names as well as English words into the path. So, for instance, we can turn PENG Shuai into Vania KING in just two steps:
PENG
PING
KING
Believe it or not, you can ROGER Federer into Rafael NADAL in six steps. You can also show that ROGER has a LEVEL head in just five steps. Also, RAFA can SAVE a point in no more than five steps, although he has to do something criminal along the way.
We’ll give you our answers at the end of the column.
Now for the new stuff. Another well-known Dodgson word game was Syzygies. (A name based on Greek that we won’t try to explain.) In this game, you again go from one word to another — but, in Syzygies, you can change as many letters as you want. Here’s the trick. You can only change letters at the beginning and end of the word. There is a core that has to stay the same. So you can’t, for instance, turn BALL into BELL, because that changes a letter in the middle of the word. You can turn BALL into ALL, or into BALK, or into BAT, or for that matter into CAT (do cats eat bats? Do bats eat cats? Wait… that’s another Carroll story). But changes must preserve the core — although the core can be only a single letter.
Note that, in Syzygies, words don’t have to be the same length. For example, you can turn BALL into NET as follows:
BALL
MALL
MET
NET
Note, however, that you can’t use this route:
BALL
BAT
BET
NET
That route involves changing an interior letter, which is forbidden. You can, however, use this route:
BALL
BAT
NET
The first change keeps the core of BAt, the second the core of neT.
Changing IN to OUT is pretty easy:
IN
IT
OUT
Or
IN
ON
OUT
The trick here is to minimize your score. Every letter you use that is not in the core counts against you. (Well, we’re simplifying this; Carroll’s scores are harder to keep, but you can look those rules up online if you want.) Let’s take the two examples we showed above for BALL and NET. The first one is BALL, MALL, MET, NET. To go from BALL to MALL, you put in one new letter, M. To go from MALL to MET, you bring in two new letters, ET. To go from MET to NET has one new letter, N. So the score in that case is one plus two plus one, for a total of four.
Now let’s go there using BALL, BAT, NET. The first change is BALL to BAT, one new letter (T). Then from BAT to NET. Two new letters, NE. So the total score for that route is three.
Try this one. Turn UMPIRE into DUMMY. (Sorry, officials….) It’s surprisingly easy:
UMPIRE
DUMP
DUMMY
Except… UM is common to both words, so in fact it’s a one-step change:
UMPIRE
DUMMY
OK, now your turn. Turn PLAYER into DUMMY. (Hey, we’re equal-opportunity insulters.) Try that, and then think of your own.
SOLUTIONS
To turn PLAYER into DUMMY can be done in two steps, believe it or not:
PLAYER
PLUM
DUMMY
or even
PLAYER
PLAY
DUMMY
As for all the doublets, the solutions are as follows:
Turn WET into DRY in no more than five steps.
The author’s first thought on this one involved the Scots word WAT (a verb, to know):
WET
WAT
WAY
WRY
DRY
A path that uses all “proper” English words is
WET
PET
PAT
PAY
PRY
DRY
A BALL can get you to a GAME in at least two ways that are three steps long:
BALL
GALL
GALE
GAME
or
BALL
BALE
GALE
GAME
It takes just three steps to cross the BASE LINE.
BASE
BANE
LANE
LINE
You can get a LINE CALL in five steps:
LINE
MINE
MILE
MILL
MALL
CALL
You can get players to move from CLAY to HARD if you use a GOAD along the way, but it takes seven steps:
CLAY
CLAD
GLAD
GOAD
LOAD
LORD
LARD
HARD
A player with lots of SLICE can produce many SPINS:
SLICE
SPICE
SPINE
SPINS
You can make CORD into NETS in five steps:
CORD
CURD
CURS
CUTS
NUTS
NETS
or
CORD
CORS (a cor was a Hebrew unit of measure)
COTS
POTS
PETS
NETS
If you don’t hit a LET, you might hit an ACE, and that might win you a SET. There are no more than seven steps along the way.
LET
BET
BAT
OAT
OPT
APT
ACT
ACE
ACE
ACT
APT
OPT
OAT
BAT
BET
SET
Believe it or not, you can ROGER Federer into Rafael NADAL in six steps. You can also show that ROGER has a LEVEL head in just five steps. Also, RAFA can SAVE a point in no more than five steps, although he has to do something criminal along the way.
ROGER
ROVER
RAVER
RAVEL
NAVEL
NAVAL
NADAL
ROGER
ROPER
LOPER
LOVER
LEVER
LEVEL
RAFA
RAFT
RAPT
RAPE
RAVE
SAVE
Incidentally, if you feel as if the longer doublets are much harder than the shorter, you’re absolutely right. Think of it this way: If you want to try to find a path from one word to another, you have to consider all the possible words that might be along the path. Take a two letter word, say IN. There are two ways you can change this: You can change the first letter, or you can change the second letter. There are 25 different changes you can make in the first letter (AN, BN, CN, DN, EN, FN, GN, HN, JN, KN, LN, MN, NN, ON, PN, QN, RN, SN, TN, UN, VN, WN, XN, YN, ZN), or there are 25 different changes you can make in the second letter. Since you can only change one letter at a time, that means that there are 50 possible changes away from IN. Of course, most of these are not words. But you have to think about all 50 possibilities to figure that out. Then, when you make the next change, there are 50 more possibilities. (Well, technically 49, since it’s pretty stupid to make a change that undoes the change you made the first time). So the number of possible two-move paths is 50 times 49, or 2450.
Now consider a three letter word, say THE. There are 25 changes you can make to the first letter, or 25 you can make to the second, or 25 you can make to the third, for a total of 75. But now think about the second move. There are now 74 (one less than 75) changes. So, to make two moves with a three letter word involves 75 times 74 changes, or 5550 possible paths. If you make three changes, there are 410700 possible paths.
For a four letter word, there are 100 possible first moves, 99 possible second moves, 99 possible third moves, 99 possible fourth moves. That’s 9900 possible changes after two steps, 980100 after three, 97029900 after four. That’s far more words than there are in the English language.
It’s not hard to make a doublet by just sitting down with, say, a five letter word and just trying stream-of-consciousness changes. But to construct a path between two particular words, as opposed to just making one change after another, is tricky, and the longer the word, the trickier.
KEYWORDS: Tennis Doublets Wordplay
THIS WEEK IN TENNIS
THIS WEEK ON THE ATP WORLD TOUR:
Winston-Salem (250/Hard). Defending Champion: John Isner
NEXT WEEK ON THE ATP WORLD TOUR:
U. S. Open (Slam/Hard). Defending Champion: Andy Murray
STATS AND FACTS
RANKINGS
Estimated ATP World Tour Rankings
As of August 22, 2013
Rank &
Prior…Player………..Points
1..(1) Djokovic……….10980
2..(2) Nadal…………..8860
3..(3) Murray………….8700
4..(4) Ferrer………….7210
5..(5) Berdych…………5075
6..(6) Del Potro……….4740
7..(7) Federer…………4695
8..(8) Tsonga………….3470
9..(9) Gasquet…………2625
10.(10) Wawrinka………..2610
11.(11) Raonic………….2555
12.(12) Nishikori……….2405
13.(13) Haas……………2185
14.(15) Janowicz………..2113
15.(16) Almagro…………2110
16.(17) Simon…………..2040
17.(14) Isner…………..2025
18.(18) Fognini…………2025
19.(19) Cilic…………..1805
20.(20) Anderson………..1740
21.(21) Tipsarevic………1685
22.(22) Robredo…………1620
23.(23) Seppi…………..1550
24.(24) Youzhny…………1475
25.(25) Kohlschreiber……1445
26.(26) Lopez…………..1435
27.(27) Paire…………..1415
28.(28) Dimitrov………..1375
29.(30) Verdasco………..1315
30.(29) Querrey…………1310
DRAWS
Winston Salem — Week of August 19
……………….3R…………….QF………..SF
1 Berdych (WC)…..Berankis……….Berankis
14 Klizan……….bautista Agut
11 Nieminen……..(11)Nieminen
6 Querrey……….(6)Querrey……..Querrey…..Querrey
3 Isner…………Bogomolov
13 Tursunov……..(13)Tursunov……Tursunov
9 Melzer………..(9)Melzer………Melzer……Melzer
5 Paire…………(5)Paire
7 Verdasco (WC)…(7)Verdasco(WC)….Verdasco
12 Rosol……….Haase
15 Monfils……..(15)Monfils……..Monfils…..Monfils
4 Robredo………(4)Robredo
8 Monaco……….(8)Monaco
10 Dolgopolov…..(10)Dolgopolov…..Dolgopolov..Dolgopolov
16 Andujar……..Lu……………..Lu
2 Seppi………..Johnson(Q)
STATUS OF SEEDS:
1 Berdych (WC)…….WITHDREW
2 Seppi…………..lost 2R (Johnson)
3 Isner…………..WITHDREW
4 Robredo…………lost 3R (Monfils)
5 Paire…………..lost 3R (Melzer)
6 Querrey
7 Verdasco (WC)…….lost QF (Monfils)
8 Monaco…………..lost 3R (Dolgopolov)
9 Melzer
10 Dolgopolov
11 Nieminen……….lost 3R (Querrey)
12 Rosol………….lost 2R (Haase)
13 Tursunov……….lost QF (Melzer)
14 Klizan…………lost 2R (Bautista Agut)
15 Monfils
16 Andujar………..lost 2R (Lu)
U. S. Open — Week of August 26
1 Djokovic
Berankis
Becker
Rosol
Kubot
Nieminen
Sousa
25 Dimitrov
24 Paire
Bogomolov
Smyczek (WC)
Duckworth (WC)
Zopp
Granollers
Ram
16 Fognini
12 Haas
Mathieu
Lu
Gimeno-Traver
Goffin
Dolgopolov
Mahut
21 Youzhny
29 Melzer
Donskoy
Sijsling
Qualifier (Q)
Hewitt
Baker (WC)
Garcia-Lopez
6 Del Potro
3 Murray
Llodra
Hanescu
L Mayer
Qualifier (Q)
Klizan
F Mayer
28 Monaco
20 Seppi
Malisse
Lacko
Qualifier (Q)
Kamke
Johnson
Istomin
15 Almagro
9 Wawrinka
Stepanek
Blake
Qualifier (Q)
Baghdatis
Qualifier (Q)
Brands
17 Anderson
31 Benneteau
Przysiezny
Stakhovsky
Chardy
Vesely
Kudla
Lorenzi
5 Berdych
8 Gasquet
Russell
Qualifier (Q)
Qualifier (Q)
Struff
Rufin (WC)
Bedene
32 Tursunov
23 Lopez
Qualifier (Q)
De Schepper
Klahn (WC)
Andujar
De Bakker
Qualifier (Q)
10 Raonic
14 Janowicz
Qualifier (Q)
Sock
Qualifier (Q)
Kuznetsov
Sela
Cuevas
18 Tipsarevic
30 Gulbis
Haider-Maurer
Qualifier (Q)
Qualifier (Q)
Bautista Agut
Bellucci
Qualifier (Q)
4 Ferrer
7 Federer
Zemlja
Giraldo
Berlocq
Zeballos
Mannarino
Pella
26 Querrey
19 Robredo
Matosevic
Haase
Qualifier (Q)
Ramos
Tomic
Qualifier (Q)
11 Nishikori
13 Isner
Volandri
Ungur
Monfils
Montanes
Roger-Vasselin
Altamirano (WC)
22 Kohlschreiber
27 Verdasco
Dodig
Williams (WC)
Davydenko
Qualifier (Q)
Pospisil
Harrison (WC)
2 Nadal
SCORES
THURSDAY
Winston-Salem
Singles – Quarterfinal
(6) S Querrey def. R Berankis 6-3 6-4
(15) G Monfils def. (7) F Verdasco 6-7(8-10) 6-4 6-4
(9) J Melzer def. (13) D Tursunov 6-4 6-3
(10) A Dolgopolov def. Y Lu 7-6(7-2) 6-3
********
TODAY’S WOMEN’S NEWS
New Haven
Here’s something you don’t see too often: An event halted both by flood and fire. Flood, as in a long rain delay. And fire, as in a small fire in the players’ area. It was quickly put out, and didn’t really affect the schedule, but what a day….
Singles – Quarterfinal: (3) Petra Kvitova def. Anastasia Pavlyuchenkova 2-6 6-2 7-5
This was not exactly what they needed on a day when the weather messed everything up. It took almost two and a quarter hours — and would have been longer had not Anastasia Pavlyuchenkova blown three points to take it to a third set tiebreak. But then, Petra Kvitova seems to think that winning efficiently is beneath her or something. She still needs one moe win to assure her Top Ten spot, but at least the points are counting. She leaves Anastasia Pavlyuchenkova still a little below #30.
Singles – Quarterfinal: (4) Caroline Wozniacki def. (6) Sloane Stephens 7-6(8-6) 6-2
Could this event finally be bringing Caroline Wozniacki back to life? She hasn’t moved in the rankings, but at least she’s winning. Sloane Stephens will not make the Top Fifteen unless Marion Bartoli’s name goes off the rankings.
Singles – Quarterfinal: Klara Zakopalova def. Elena Vesnina 4-6 6-0 6-4
It looks as if this will put Klara Zakopalova in the Top Thirty. It’s a big result for her, given her historical lack of liking for hardcourts.
Singles – Quarterfinal: Simona Halep def. Ekaterina Makarova 6-1 7-6(8-6)
It’s amazing Simona Halep hasn’t moved in the rankings yet; it seems as if nothing can stop her. Ekaterina Makarova will probably be right at #25.
THIS WEEK IN TENNIS
THIS WEEK ON THE WTA:
New Haven (Premier/Hard). Defending Champion: Petra Kvitova
NEXT WEEK ON THE WTA:
U. S. Open (Slam/Hard). Defending Champion: Serena Williams
STATS AND FACTS
RANKINGS
Estimated WTA Rankings As of August 22, 2013
Rank &
Prior
Rank….Name…………..Points
1..(1) SWilliams ……… 12260
2..(2) Azarenka ………..9505
3..(3) Sharapova ……… 8766
4..(4) RAadwanska ………6335
5..(5) ERRANI ………….5125
6..(6) Li ……………..4825
7..(7) Bartoli ……….. 4246
8..(8) WOZNIACKI ……… 3490*
9.(10) KERBER ………….3420
10.(13) Stosur ………….3210
11..(9) KVITOVA ……….. 3170*
12.(11) Jankovic ………..3125
13.(12) VINCI …………. 3065
14.(14) Flipkens ………..2961
15.(15) Ivanovic ………..2940
16.(17) STEPHENS ………..2925
17.(16) Kirilenko ……… 2620
18.(18) LISICKI ……….. 2615
19.(20) SUAREZ NAVARRO …..2375
20.(19) CIBULKOVA ……… 2281
21.(21) CIRSTEA ……….. 2250
22.(22) Petrova ……….. 2212
23.(23) HALEP …………. 2180*
24.(24) VESNINA ……….. 2127
25.(26) MAKAROVA ………..1935
26.(25) Hampton ……….. 1881
27.(27) Kanepi ………….1781
28.(28) Cornet ………….1730
29.(29) Kuznetsova ………1679
30.(33) ZAKOPALOVA ………1600
DRAWS
New Haven — Week of August 19
……………..QF……………SF
1 Errani………Makarova
5 Vinci……….Halep…………Halep
4 Wozniacki……(4)Wozniacki…..Wozniacki
6 Stephens (WC)..(6)Stephens(WC)
7 Lisicki……..Pavlyuchenkova
3 Kvitova……..(3)Kvitova…….Kvitova
8 Cibulkova……Zakopalova…….Zakopalova
2 Kerber………Vesnina
STATUS OF SEEDS:
1 Errani……….lost 2R (Makarova)
2 Kerber……….lost 2R (Vesnina)
3 Kvitova
4 Wozniacki
5 Vinci………..lost 1R (Suarez Navarro)
6 Stephens (WC)…lost QF (Wozniacki)
7 Lisicki………lost 2R (Pavlyuchenkova)
8 Cibulkova…….lost 1R (Knapp)
U. S. Open — Week of August 26
1 Williams
Schiavone
Voskoboeva
Niculescu
Shvedova
Puchkova
Qualifier (Q)
29 Rybarikova
23 Hampton
Arruabarrena
Mladenovic
Medina Garrigues
Begu
U Radwanska
Minella
15 Stephens
12 Flipkens
V Williams
Bertens
Zheng
Qualifier (Q)
Qualifier (Q)
Davis
18 .Suarez Navarro
25 Kanepi
King (WC)
Voegele
Schmiedlova
Ka Pliskova
Bouchard
Hradecka
8 Kerber
3 A Radwanska
Soler-Espinosa
Torro-Flor
Erakovic
Cabeza Candela
Barty (WC)
Razzano (WC)
32 Pavlyuchenkova
24 Makarova
Hercog
Johansson
Mattek-Sands
Ormaechea
Date-Krumm
Qualifier (Q)
16 Lisicki
9 Jankovic
Keys
Puig
Kleybanova
Qualifier (Q)
Cadantu
Qualifier (Q)
19 Cirstea
30 Robson
Dominguez Lino
Garcia
Rogers (WC)
Cetkovska
Arvidsson
Govortsova
5 Li
6 Wozniacki
Qualifier (Q)
Scheepers
Qualifier (Q)
Cepelova
Qualifier (Q)
Hsieh
31 Zakopalova
22 Vesnina
Beck
Knapp
Qualifier (Q)
Tsurenko
Safarova
Babos
10 Vinci
14 Kirilenko
Wickmayer
Qualifier (Q)
Daniilidou
Vekic
Duque-Marino
Watson
21 Halep
27 Kuznetsova
Burdette
Peng
Meusburger
Gibbs (WC)
Pennetta
Morita
4 Errani
7 Kvitova
Doi
Jovanovski
Petkovic
Pironkova
Riske (WC)
Larsson
28 Barthel
20 Petrova
Qualifier (Q)
Qualifier (Q)
Vickery (WC)
Sanchez (WC)
Hantuchova
Qualifier (Q)
11 Stosur
13 Ivanovic
Tatishvili
Lepchenko
Dulgheru
Goerges
McHale
Svitolina
17 Cibulkova
26 Cornet
Qualifier (Q)
Qualifier (Q)
Qualifier (Q)
Wozniak
Dolonc
Pfizenmaier
2 Azarenka
SCORES
THURSDAY
New Haven
Singles – Quarterfinal
(3) Petra Kvitova def. Anastasia Pavlyuchenkova 2-6 6-2 7-5
(4) Caroline Wozniacki def. (6) Sloane Stephens 7-6(8-6) 6-2
Simona Halep def. Ekaterina Makarova 6-1 7-6(8-6)
Klara Zakopalova def. Elena Vesnina 4-6 6-0 6-4
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