In mathematics, addition is subject to the Commutative Law.  That is, if 2+3=5 then we may also say 3+2=5… unless you work at the local Wegmans grocery store.

I was in the cashier’s line behind a matronly woman whose order the young girl at the register was finishing up.  The girl announced. “That will be $104.62 today.”  The woman thumbed through her wallet and extracted a $50 bill and three crisp $20s, which she handed to the cashier.

The girl promptly started counting the money out, announcing her total as she went.  “50, 70, 90, 100,” she said.  Upon completion, she turned to the woman and  reminded her of the total.  The woman smiled sweetly at the young lass and suggested that perhaps she could count it out again.  Once more the girl confidently said, “50, 70, 90, 100.”  This time she ended with, “You’re still short $4.62.”

The woman was maintaining her composure, but looked as if she really wanted to grab the sweet thing by her pigtails and say something that started with, “LISTEN MISSY!”  To her credit, she instead asked the girl how much the three $20s were worth.

Fanning the bills in her hand the cashier said, “$60.”

“And how much is 60 plus 50,” the patient woman softly inquired?

You could almost see the wheels of the poor young girl’s mind grind to a halt as the pain of this dawning contradiction came across her.  With renewed determination, she grasped the short stack of bills and began counting aloud again.  “50, 70, 90, 100.”

In an effort to be helpful, I offered that perhaps she should start counting with the $20s.  The girl’s face brightened momentarily, and she flipped the stack and started counting yet again.  “20, 40, 60, 110.”  She looked positively delighted with herself while the poor woman in line just imperceptibly shook her head.

The cashier now looked at me and asked, “So why doesn’t it work when I do it the other way?”

I offered, somewhat less helpfully, “I guess it’s just one of those math mysteries no one understands.”  An explanation the young girl seemed quite satisfied with as she finally began to count change.  However, the matronly woman lowered her head and gave me a look over her glasses that was oddly reminiscent of my high school geometry teacher who also took it upon herself to make it clear to me that I was not nearly as amusing as I imagined.

Not wishing to push my luck, I paid for my order with a credit card.