Miss Silverwood, a matronly woman wearing sensible shoes, clomped into the classroom.  Her dress was printed dimly with dots or possibly daffodils.  From atop her head, horn-rimmed spectacles stared eyelessly upward.  Gray strands tethered a balloon of frazzled hair to the back of her head.  She unshouldered a slumping purse onto the floor and studied the blackboard, while students stifled giggles and tried instead to breathe.

“Your thoughts are not your own,” proclaimed Miss Silverwood in a strong and surprisingly melodious voice.  She erased the blackboard and wrote her name in cursive script.  “I have the power to perceive your every thought at will.”   Miss Silverwood turned to face the class.  She gazed for what seemed like a full minute into unblinking eyes. “Yes, I am your substitute teacher, and no, Mr. Johnson himself will explain on Monday why he is not here today.” 

Perhaps the students sensed that an unforgettable hour was beginning.

“Some of you are thinking that I have just made an impossible claim,” she said, surely not for the first time. “At this very moment, you are thinking, ‘No person can know the thoughts of another’.”  She allowed part of her face to smile. “I will not ask you to raise your hands, for I know who you are -- the skeptics in this class. And you will not accept extraordinary claims without evidence, am I right?” 

The only sounds were street noises outside the classroom window.  “Even now, I know what you are thinking.  You are thinking I should not need to ask, ‘Am I right?’ for, if I really can perceive your thoughts, then I would know I am right.  And, of course, you are right to think that.  However, I am prepared today to offer mathematical proof of my paranormal powers.”

iss Silverwood watched the students exchanging glances.  “You are all invited to write down a decimal number.”  Several hands shot skyward.  “Don’t bother asking questions,” she said.  “Yes, your number can be any size you want, and, as for your other question, no, please make it an integer – a whole number.”  The students put down their hands. 

“Next create a new integer,” said Miss Silverwood. “This time, simply mix up the digits in your first integer.  And yes, you will use all the digits in your new integer that you used in your first one.”  She paused for scribbling to stop.  “Now, calculate the arithmetic difference between the two integers.  That’s right, subtract one from the other.  Some of you will get a negative number, but, being algebra students, you won’t worry much about that.” 

“Take a moment to look at your difference there,” she said.  “Here is what I want you to do: Select one of its digits and cross it out -- cross it out completely, but keep that digit firmly in your mind.  Finally, scramble the rest of the digits and write them down in a row – with your selected digit removed.” 

Miss Silverwood squinted her eyes trance-like.  “Keep concentrating on the digit that you selected.  Ah, you are doing just fine,” she said, “I am perceiving your selected digits, every one of them.  There are several eights in the room, some fives, and a few -- ” 

The students interrupted with laughter. 

“You think I am joking,” said Miss Silverwood.  Taking chalk in hand, she pointed at the student with the biggest grin.  “Please read me your scrambled number – and, no, do not include your selected digit.”  She wrote the number on the blackboard, then turned quickly and announced, “Your selected digit is seven!” 

The student stopped grinning.  Audible gasps replaced laughter. 

Miss Silverwood nodded toward a girl in the front row.  “And how about yours?” she asked.  After writing the girl’s scrambled number on the blackboard, Miss Silverwood mused aloud, “You have no secrets from me, young lady.  Your selected digit is – well, it is three.  And how about you?” she asked, abruptly pointing to a boy at the back of the room.

In a matter of minutes, astonished students called out numbers of varying lengths.  The blackboard filled up.  Miss Silverwood correctly identified every selected digit that day in a triumph of paranormality.  Or so it seemed.