THE SPOT ON THE TABLE.
(
Money Puzzles)
A boy, recently home from school, wished to give his father an
exhibition of his precocity. He pushed a large circular table into the
corner of the room, as shown in the illustration, so that it touched
both walls, and he then pointed to a spot of ink on the extreme edge.
"Here is a little puzzle for you, pater," said the youth. "That spot is
exactly eight inches from one wall and nine inches from the other. Can
you tell me the diameter of the table without measuring it?"
The boy was overheard to tell a friend, "It fairly beat the guv'nor;"
but his father is known to have remarked to a City acquaintance that he
solved the thing in his head in a minute. I often wonder which spoke the
truth.
Answer:
The ordinary schoolboy would correctly treat this as a quadratic
equation. Here is the actual arithmetic. Double the product of the two
distances from the walls. This gives us 144, which is the square of 12.
The sum of the two distances is 17. If we add these two numbers, 12 and
17, together, and also subtract one from the other, we get the two
answers that 29 or 5 was the radius, or half-diameter, of the table.
Consequently, the full diameter was 58 in. or 10 in. But a table of the
latter dimensions would be absurd, and not at all in accordance with the
illustration. Therefore the table must have been 58 in. in diameter. In
this case the spot was on the edge nearest to the corner of the room--to
which the boy was pointing. If the other answer were admissible, the
spot would be on the edge farthest from the corner of the room.
Informational
