PUZZLES
1) Create a square consisting of four rows and four columns. Each “box” in the square contains a different number from one through 16. Every number appears only once. The sum of every row is identical; likewise the sum of every column, quadrant, the diagonals, and the sum of the central four boxes.
2) Why is a raven like a writing desk? Or, if Lewis Carroll’s famous conundrum doesn’t appeal to you, then answer this gentle query: you’re at a party. Can everyone at the party have a different number of friends present? For greater certainty, a person can’t be his or her own friend, and someone may have no friends.
The answers to January’s puzzles were supplied in the January issue.
Here are the answers to this month’s puzzles:
1) Hint: Albrecht Durer engraved a picture of this square, and the date of his engraving lies in the bottom row, central two boxes.
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
2) As to Lewis Carroll, he didn’t supply an answer, perhaps because there’s a “b” in both and an “n” in neither. As to friends and gatherings, at least two people will have the same number of friends at the party. The reason is that a friend is defined as someone else, not one’s self. In math terms, we can identify each person with a different number from A through (say) J. Assume person A has no friends in the gathering, person B has one friend, and so forth, through J who has J – 1 friends. But there is a contradiction between J, who counts A as a friend, and A, who claims to have none. To avoid the contradiction, J must have the same number of friends as one of the other people (J – 2 friends, or J – 3 friends, for example). Lest the issue of zero seem relevant, eliminate it and the result is the same. A has one friend, B has two, and so forth through J, who has ten. But this ten includes him or herself, which is excluded. J must therefore have the same number of friends as one of the other partygoers.
