square; and I doubt whether there are two of exactly the same size. If only I knew the size of the field I could soon discover it, and, by taking these simple measurements, quickly secure the treasure."

66 6

'But you would not know which corner to start from, nor which direction to go to the next corner.'

66

"My dear chap, that only means eight spots at the most to dig over; and as the paper says that the treasure is three feet deep, you bet that wouldn't take me long.'

"Now, gentlemen," continued Dawkins, "I happen to be a bit of a mathematician; and, hearing the conversation, I saw at once that for a spot to be exactly two, three, and four furlongs from successive corners of a square, the square must be of a particular area. You can't get such measurements to meet at one point in any square you choose. They can only happen in a field of one size, and that is just what these men never suspected. I will leave you the puzzle of working out just what that area is.

"Well, when I found the size of the field, I was not long in discovering the field itself, for the man had let out the district in the conversation. And I did not need to make the eight digs, for, as luck would have it, the third spot I tried was the right one. The treasure was a substantial sum, for it has brought me home and enabled me to start in a business that already shows signs of being a particularly lucrative one. I often smile when I think of that poor fellow going about for the rest of his life saying: 'If only I knew the size of the field!' while he has placed the treasure safe in my own possession. I tried to find the man, to make him some compensation anonymously, but without success. Perhaps he stood in little need of the money while it has saved me from ruin."

Could the reader have discovered the required area of the field from those details overheard in the wineshop? It is an elegant little puzzle, and furnishes another example of the practical utility, on unexpected occasions, of a knowledge of the art of problemsolving.

0

THE PROFESSOR'S PUZZLES

"Why, here is the Professor !" exclaimed Grigsby. "We'll make him show us some new puzzles."

It was Christmas Eve, and the club was nearly deserted. Only Grigsby, Hawkhurst, and myself, of all the members, seemed to be detained in town over the season of mirth and mincepies. The man, however, who had just entered was a welcome addition to our number. "The Professor of Puzzles," as we had nicknamed him, was very popular at the club, and when, as on the present occasion, things got a little slow, his arrival was a positive blessing.

He was a man of middle age, cheery and kind-hearted, but inclined to be cynical. He had all his life dabbled in puzzles, problems, and enigmas of every kind, and what the Professor didn't know about these matters was admittedly not worth knowing. His puzzles always had a charm of their own, and this was mainly because he was so happy in dishing them up in palatable form.

"You are the man of all others that we were hoping would drop in," said Hawkhurst. "Have you got anything new?

?"

"I have always something new," was the reply, uttered with feigned conceit for the Professor was really a modest man- —“I'm simply glutted with ideas."

66

'Where do you get all your notions ?" I asked.

"Everywhere, anywhere, during all my waking moments. Indeed, two or three of my best puzzles have come to me in my dreams."

66

99

Then all the good ideas are not used up "Certainly not. And all the old puzzles are capable of improve

ment, 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."

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."

66

"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 ? "

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."

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Here you are!" cried Grigsby, after he had been scribbling for a few minutes on the back of an envelope.

The Professor smiled indulgently.

66

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.”