I was out and about yesterday and so am not in position to award the gold medal for most absurd defense of President Trump during the full House's impeachment debate, but while driving I did hear on the car radio one guy quote Jesus on the cross, "Forgive them Father, for they know not what they do," before assuring Democrats that, following Christ's example, he was praying for them in just the same way. I thought this was, you know, over the top by an inch or two, and this morning, trying to track down the identity of the biblical scholar, I kept getting referred by Google to some other representative who had compared the Democrats unfavorably to Pontius Pilate. If Minority Leader McCarthy hadn't been working so hard on his own floor speech, it might have occurred to him to import a Gospel choir to sing, during the interval when representatives were voting electronically to impeach Trump, "Where Were You When They Crucified My Lord?"

I was sitting at the dining room table being perplexed by a math test that Lydia, my 6th grader, had brought home from school. The problem she got wrong is pictured above. Let's see, if Jim had $4 Peter would have $7, then Peter gives Jim three-fourteenths of $7, which is a buck fifty, and they both have $5.50, so that must be the answer, except that if Jim had $8 then Peter had $14, and Peter would then give Jim $3, in which case they'd both have $11, so I guess there are at least two "right" answers, and if there are two maybe there are a billion more!

Poor Lydia. As she pointed out, "I tried," but she's only in 6th grade and could never have figured out that the correct answer is: "My math teacher might be a little weak at math, maybe he should read up on the New Testament and run for Congress, he's more than smart enough and the salary is $174,000 per year."

UPDATE: A fellow math geek writes to defend Lydia's teacher, on the theory that the above problem is a kind of trick question, and that the right answer is that Jim could have started with any amount of money—which is indeed the right answer to the problem as it was set out on Lydia's test.

I meant to insult Bible-thumping congressmen, not middle school math teachers, who, being overworked and underpaid, might pull the deficient (or trick) problem from some source available to math teachers. If so, and the source provides answers to its suggested problems, I'd be curious about the solution it gives for the one about Jim and Peter. I told my geeky friend that I think the direction "Show all work" indicates the problem is deficient, not a "trick," but I could be wrong. If instead of a test question this problem had been homework, and Lydia had asked for help, we could have gotten to the bottom of everything by turning in a paper that said:

*Jim could have started with any amount of money. Let x stand for however much he had to start, then Peter started with 7x/4 dollars. Subtract from Peter's 7x/4 dollars (3/14)(7x/4) and add to Jim's x dollars the same amount. Peter then has 7x/4 — (3/14)(7x/4) = 7x/4 — 21x/56 = 14x/8 — 3x/8 = 11x/8. And Jim has the same amount: x + (3/14)(7x/4) = x + 21x/56 = x + 3x/8 = 11x/8. *

I think that's a good answer. It's "correct" if it's a "trick" question and, if it's not meant as a trick question, it shows that something's gone wrong. That the fractions are a little unwieldy helps to disguise what I take to be an error. Suppose the problem had been:

*Peter has twice as much money as Jim. After he gives a quarter of his money to Jim, they have the same amount. How much did Jim have to start?*

Same principle, but it's easier to see that Jim could have started with any amount.