“Yes,” Ernie admitted: “a different answer every day.”

The problems in question were certainly difficult. There were ten of them,—ingeniously composed by “the Visiting Board”; and it was rumoured among the girls that even Miss Horton, herself, could not obtain a correct solution. They were intended for practice-work during the term, on the express understanding that one of the set, no one could predict which, should be included in the final examinations.

Naturally, they were the subject of much and anxious discussion. Lulu Jennings, in particular, suffered agonies of apprehensive doubt. Arithmetic is not her strong point.

“I don’t think it’s fair,” she declared. “He just meant to muddle us. The idea of making up such stuff out of his own head! There isn’t any key, or any way to prove ’em, and the answers are not even in the back of Miss Horton’s teacher’s book. I know, because——”

“Because?” questioned Mary Hobart. And Lulu dropped her eyes, and coloured uncomfortably.

It was after her public disgrace that Ernie wrote out the entire set of problems in a blank-book purchased for the purpose, so that she might study them quietly at home. And how the child did wrestle!—shutting herself in the workshop Saturday after Saturday, till finally she discovered the correct solution! There could be no doubt. Worked out along certain intricate lines the problems could be proved!

The next morning, which happened to be the very day before examination, Ernie carried her precious book down to school.

Coo-ee!” she yodeled to Mary Hobart, who formed one of a group of chattering girls on the second landing. “I have the answers!”

“Not to the Visiting Board’s problems?” returned Mary, excitedly.

“Yes,” Ernie replied, unable to repress her glee. “They are here!” tapping the book as she spoke. “And they are right, too. They prove!—all those I’ve had time for!”