“Just think of a number――any number――and write it down on the envelope and multiply it by three.” Miss Johnson, conscious that all eyes were fixed upon her, did the necessary sum. “Well?” she said. “Add one to it, and then multiply the result by three again.” “I hope this is all,” said Miss Johnson severely, while at the same time she cast a penetrating glance round the assembled company. She noted in particular the solemn gaze of Ann and Jim, and immediately her suspicions in regard to a trap were confirmed. “Very nearly. Now add the original number you chose.” “No, Palmer: this will go on for ever! I haven’t time. Besides, you can get one of the others to do it;”――and she gave the paper and pencil to Ann. “Come, Barbara, we must hurry. The shops close early to-day.” Palmer submitted politely, while Miss Johnson, satisfied that, if any foolish joke had been intended, it had failed, withdrew, taking Barbara with her. “What am I to do, Balmer?” Ann asked. “Oh, just add the original number to what you have there. The original number will be the first one of all.” “But what do I add it to?” “Here, show it to me,” said Edward brusquely, taking the paper out of her hand. “Right you are, Dorset. This is a very ancient trick.” “I didn’t say it was new,” replied Palmer, yawning, “but if you read out the result it may have answered its purpose.” “What purpose? Three-forty-three.” “The purpose of finding out that Miss Johnson’s age is thirty-four. Ann wanted to know.” “Oh, Balmer, how frightfully clever of you!” cried Ann, in ecstasies. “It’s all swank!” exclaimed Edward, incredulously. “You can’t get a person’s age that way. It just gives you whatever number they happen to choose. It’s an old thing out of the _Boy’s Own Paper_.” “That’s all that is wanted,” said Palmer. “What is the first number that is most likely to come into Miss Johnson’s head to-day? Her age. I don’t say that it’s sure to be right; but I’ll bet three to one in tins of toffee that it is. Will you take it on?” “No,” replied Edward simply; “it isn’t profitable to bet with you, Dorset: you’re too fond of certainties.” “It isn’t a certainty. You know as much about it as I do. The only difference is that I’m willing to back my opinion, and you aren’t.” “Well, I’m not going to bet anyway.” “I think you ought to apologize for that remark about certainties.” “All right: I take it back.” “But I can’t put thirty-four candles on the cake,” Ann said sadly. “It isn’t nearly big enough.” “I tell you what,” cried Jim. “We’ll let off thirty-four rockets.... Only we haven’t enough, unless we take down the set-piece.” Then he had a bright idea. “I’ll go and tell Aunt Caroline what it’s for, and she’ll maybe give me the money to buy the extra rockets.” He was off before anyone had time to speak, but in a very few minutes he came back, looking rather crest-fallen.