"Certainly not. And all the old puzzles are capable of improvement, embellishment, and extension. Take, for example, magic squares. These were constructed in India before the Christian era, and introduced into Europe about the fourteenth century, when they were supposed to possess certain magical properties that I am afraid they have since lost. Any child can arrange the numbers one to nine in a square that will add up fifteen in eight ways; but you will see it can be developed into quite a new problem if you use coins instead of numbers." [Illustration] 67.--_The Coinage Puzzle._ He made a rough diagram, and placed a crown and a florin in two of the divisions, as indicated in the illustration. "Now," he continued, "place the fewest possible current English coins in the seven empty divisions, so that each of the three columns, three rows, and two diagonals shall add up fifteen shillings. Of course, no division may be without at least one coin, and no two divisions may contain the same value." "But how can the coins affect the question?" asked Grigsby. "That you will find out when you approach the solution." "I shall do it with numbers first," said Hawkhurst, "and then substitute coins." Five minutes later, however, he exclaimed, "Hang it all! I can't help getting the 2 in a corner. May the florin be moved from its present position?" "Certainly not." "Then I give it up." But Grigsby and I decided that we would work at it another time, so the Professor showed Hawkhurst the solution privately, and then went on with his chat. 68.--_The Postage Stamps Puzzles._ "Now, instead of coins we'll substitute postage-stamps. Take ten current English stamps, nine of them being all of different values, and the tenth a duplicate. Stick two of them in one division and one in each of the others, so that the square shall this time add up ninepence in the eight directions as before." "Here you are!" cried Grigsby, after he had been scribbling for a few minutes on the back of an envelope. The Professor smiled indulgently. "Are you sure that there is a current English postage-stamp of the value of threepence-halfpenny?" "For the life of me, I don't know. Isn't there?" "That's just like the Professor," put in Hawkhurst. "There never was such a 'tricky' man. You never know when you have got to the bottom of his puzzles. Just when you make sure you have found a solution, he trips you up over some little point you never thought of." "When you have done that," said the Professor, "here is a much better one for you. Stick English postage stamps so that every three divisions in a line shall add up alike, using as many stamps as you choose, so long as they are all of different values. It is a hard nut." [Illustration] 69.--_The Frogs and Tumblers._ "What do you think of these?"