A Squeeze at the Penultimate Trump

On the pictured hand 13 at the Pembury Bridge Club in Pittsfield MA on Wednesday June 14, 2017, as East I made 3S, losing a trick in each suit. After ducking the heart lead and winning the continuation, I could have made 4 by reaching a position with DA5 and H7 in my hand, DJ8 and CJ on the board, and South down to HQ and DQT. Leading my heart endplays South in Diamonds. Peter Winkler explained to me how to make 4 on a Club lead (the previous endplay cannot afford a club loser). After losing e.g. a Club, a Heart, and a Spade, play Spades from dummy, coming down to S53, DJ84 in dummy. Now on the penultimate spade, come down to DAK, Hxx in hand, and South cannot protect both Diamonds and Hearts. (If North leads a Diamond when he gets in with a Club, East will be left with the HA as the second entry to hand. Play Spades in a way to prevent North from getting in to lead Diamonds twice. Curiously, when they start with Hearts, you need to play Spades the other way to prevent South from giving North a Heart ruff.)

Amazing AMS spring sectional in Pullman WA

I just attended an amazing constellation of events around the AMS spring sectional meeting Saturday/Sunday April 22-23, 2017, in Pullman, Washington, organized by Kevin Vixie of Washington State University.

The meeting was preceded by a day on Data Science, with an incredible variety of short talks every 15 minutes, interspersed with discussion periods. Continue reading ‘Amazing AMS spring sectional in Pullman WA’ »

The Life of an Adjunct

Guest post by Donna Kalinowsky

Dear Community College President,

Perhaps you do not know what life is like for an adjunct. When I started here in 1992 or so, I made about $9000 per year. Even then, that was not much. I was eligible for Section 8 housing, food stamps, fuel assistance, Medicaid, head start for my kids, access to local food pantries, Christmas Elf programs for children’s gifts, and the Earned Income credit. Thanks to these things, I was able to raise 4 children, ages 29, 27, 14 and 9. Continue reading ‘The Life of an Adjunct’ »

Aldo’s Diary

I set out to write a novel, and ended up with this short story draft. Thanks to Mary Collins for some editing. Comments most welcome.

ALDO’S DIARY by Frank Morgan

“Mom, Penny beat me at chess.” Penny’s mother, Elizabeth Murrow, stopped loading the clothes washer and stopped thinking about triangles in the hyperbolic plane.


“Yes, I did — I beat Aldo at chess. And he’s two years older than me.”

“But I thought you said you weren’t any good at games.”

“I didn’t think I was.”

“Aldo, did you let her win?”

“She forked my king and my rook.”

“Penny, you forked his king and his rook?”

“Yes, I planned it, like Dad did to me last night. I attacked his king and his rook at the same time with my knight, and since he had to move his king, I got his rook.”

Click here to continue reading

Retirement Book

screen-shot-2016-11-15-at-8-14-53-amHeartfelt thanks to Brooks Foehl/Alumni Office and especially to my students for their kind remembrances upon my retirement:

Back in Granada

img_2014Back in Granada on my way to Alicante, staying once again at university residence Carmen de la Victoria, I revisited the site of a 13-year-old diary entry, dated June 15, 2003:

A dusty pedestrian road by the Alhambra is lined with engraved quotations. My favorite on Saturday was by Thoreau, translated into Spanish. Here are my own English version constructed from memory as I continued my walk, followed by the English original which I later found on the web, and finally my revision. Continue reading ‘Back in Granada’ »

Bridge in Buenos Aires

R24 Recoleta'16Got to fill in at last minute with Director Marcelo de Carlo at the Recoleta Bridge Club in Buenos Aires 3:30 pm Monday September 4, 2016. On the pictured Hand 2, East on my right opened 1S, I bid 2H, West passed, North bid 3H, East 4D, South 4H, West passed! and so did everyone else. West led the Spade 4 and followed with the 6 as East played K and A. It was surprising that West would pass with three spades, but I decided that W having all three hearts was more likely than false carding with two spades, so I trumped low. To pass with three spades, West must have almost nothing, so East must have the diamond A and club K. I played three rounds of trump to enter dummy and immediately led a diamond, East erring by playing low. Now when I run the hearts, leaving AQ of clubs and J of diamonds in dummy, East falls to an endplay. Unfortunately I chickened out at the last minute and took the losing club finesse.

Fortunately on the last Hand 24 I competed to 5Sx with everyone else in game the other way for 15 IMPS to tie for first.

Working at Home Depot

A guest post by Donna Kalinowsky.

I teach mathematics as an adjunct instructor at Berkshire Community College (BCC) in Massachusetts, which is one of a handful of states that does not allow its employees to pay into Social Security. To get my last requisite credits toward Social Security, I took a part-time job at Home Depot. Home Depot has taught me a lot about gratitude and dignity.

I have met several people at Home Depot who are good, smart, hard working people. I go to them often when I have an issue I can’t solve on my own. Some are part time like me, working unpredictable hours at $11 an hour. I doubt even the few full-time people earn a whole lot more. (Just like BCC, Home Depot tries to minimize full timers in order to avoid paying benefits, though Home Depot does offer some benefits to part timers if they work there long enough.)

I work there by choice, for a special reason, but for these people. This is their life. One girl has no car, so she has to take the bus to work. But if she is scheduled on a day when  no bus service is available, she has to take a cab to work. If she’s scheduled for four hours  at $11 an hour and a taxi costs $20, then it’s almost like she’s working for taxi money. Continue reading ‘Working at Home Depot’ »

More Solutions to Fermat with Fractional Exponents

Nicola Marino has offered to post the following preprint:

Irrational Exponents in Fermat’s Last Theorem. The n > 2 case.

by Nicola Marino

In this paper we find explicit irrational exponents greater than 2 solving the Fermat equation, which we call Algebraically Derived Ratio of Irrational (or ADRI) numbers. We then further expand the class of ADRI numbers to cover all the solution exponents for any Fermat equation.

Continue reading

Euler’s Theorem by Induction on Vertices

In my Discrete Math class today, Ryan Patton asked to prove Euler’s circuit theorem by induction on the number of vertices. Alex Summers contributed an idea about pairing/short-cutting instead of removing the edges incident to a deleted vertex. The class came up with the following proof. Is this proof out there somewhere?

Theorem (Euler). A pseudograph has a circuit containing all edges and vertices if it is connected and every vertex has even degree.

Proof by induction on the number n of vertices.

Base case n=1. Just follow the loops in succession.

Now assume for n and prove for a pseudo-graph of n+1 vertices. Pick a vertex. Since degree even, you can pair the incident edges, and you can avoid pairing the two ends of a loop. Short-cut each pair to avoid the vertex and delete it. By induction, each component of the new pseudo-graph has the desired circuit. Now restore the vertex and undo the short cuts to obtain the desired circuit.