If you have an Amherst liberal arts education, you are probably a logophile. Or, like Stephanie MacConnell, wife of my cherished classmate Scott MacConnell ’60, you may even be a lexophile. In either situation, you might enjoy the challenge presented here.

Using only the seven distinct letters in the word Amherst, using no letter more than once, and not including the word Amherst itself, Stephanie and I created a list of 155 words. The list contained 52 words made up of at least five letters.

I was a mathematics major at Amherst. Wonderful professors such as Robert Breusch, Bailey Brown and Atherton Sprague spurred my interest in math. The required curriculum in those days forced me into English, history and other humanities courses. Academically, I did not fare well on the verbal side, but the rigorous exposure to words prepared me for an enjoyable and successful career as a mathematics teacher—success that would have been beyond my reach without the overall Amherst experience. To this day, I am a logophile.

Using only the seven letters A, M, H, E, R, S and T, and using no letter more than once, and not using the word Amherst, and using no online tools (we want to see what you can do yourself), create as many words as you can that contain at least five letters.

THE PRIZE: an Amherst T-shirt.

Send your list to:  magazine@ amherst.edu or Amherst Magazine, Box 5000, Amherst, MA 01002.

The longest list will appear in our next issue.

By Aaron Carroll ’94, M.D., who wrote the “Math in Medicine” contest.

1. If we take a random group of 1,000 50-year-old women, how many will be expected to die of breast cancer in the next 10 years? If we screen those 1,000 women with mammograms every two years for a decade, how many fewer women might be expected to die of breast cancer?

In a random group of 1,000 50-year-old women, about five are likely to die of breast cancer in the next 10 years. If we screen every two years for a decade with mammograms, we prevent one of them from dying of breast cancer. We need to regularly screen 1,000 women in this way to prevent one breast cancer death. Studies have shown that both men and women overestimate their risk from diseases and the bene ts of screening.

2. A recent study found that 0.5 percent of women ages 50 to 69 have breast cancer. One woman in that age group goes in for a screening mammogram. She gets a call that it’s “positive” come back for a further workup. After that positive screen, what is the percent chance that she really has breast cancer, and what’s the percent chance that she does not?

Pre-mammogram, there’s a 99.5 percent chance that she does not have breast cancer. Based on the test characteristics, once she has had a “positive” screening mammogram, she then has a 4 percent chance of having breast cancer. She still has a 96 percent chance of not having breast cancer, even after the positive screen. People think that many screening tests are much more accurate than they really are.

3. Your child has an ear infection, and you’re thinking about asking for antibiotics to treat it. How many ear infections does a pediatrician need to treat with antibiotics to prevent one serious complication? How many do they need to treat with antibiotics to reduce one child’s pain within 24 hours? Within two to seven days? Finally, how many do they need to treat with antibiotics to have one child get a side effect, like vomiting, diarrhea or a bad rash?

There’s no evidence that antibiotics will prevent a serious complication or reduce pain within 24 hours. A doctor needs to treat 20 children with antibiotics for one to have significantly improved pain in two to seven days; the other 19 see no benefit. But a doctor only needs to treat 14 with antibiotics to see one get a side effect. Therefore, it’s arguable that your child might be more likely to see a side effect than a benefit. For most children with ear infections, the American Academy of Pediatrics recommends observation with close follow-up.

Congratulations to the two winners of our "Math in Medicine" contest, Boruch Fishman ’71, M.D., and Christine Petrecca Weintraub ’84, M.D. Each will receive an Amherst T-shirt.