It's a Puzzlement: Scrambled Addition

Chris Yaure writes, "Recently I attempted to copy part of a spreadsheet into a text document. Unfortunately, the word processor converted all of the digits into letters. This is what I saw:

		C	A	S	U	A	L	.	T	Y
+	A	C	T	U	A	R	I	.	A	L
______________________________________________________________________________
	S	O	C	I	E	T	Y

I was surprised to discover that each letter had replaced the same numeral each time the letter appeared. Upon reviewing the documents further, I realized that the original numbers had contained no zeros, and that each numeral from 1 to 9 was represented by at least one letter (two numerals were represented by two different letters). Finally, one of the pairs of letters that replaced the same numeral is A and Y." Can you unscramble Chris' computation?

Replace the King

This was a difficult problem. For those of you who were stumped, here is the solution. We will give moves in algebraic notation. Squares are referred to by a letter-number combination, such as c5. The letter gives the file (column) with the leftmost file as a, through to the rightmost as h. The bottom rank (row) is 1, and the top rank is 8. Thus the lower left corner is a1, and the top right corner is h8. Start with pieces as shown in the diagram (the black bishop could be anywhere along the a8-h1 diagonal, except at d5). It is black's turn to move. This is a position that could be reached with legal play. Note the addition of two pawns; they will be the key to the solution.

Moves proceed as follows: black moves the bishop to d5, putting the white king in check. White moves its pawn to c4, blocking the check. Black takes the white pawn en passant by moving its pawn to c3. This puts the white king in double check, both from the bishop and the rook. White takes the black pawn on c3 with the king. Thus the white king should be replaced on c3, and it is black's move. A process of elimination can be used to show that this is the only solution.

Solutions were submitted by Jeff Dvinoff, Madelyn Faggella, Steve Fallon, Moshe Goldberg, John Herder, Aaron Newhoff, Charles Petrizzi, Bill Saffran, Dave Schofield, Gregory Scruton, Dave Skurnick, Joe Theisen, and (jointly) Jeff Subeck and A. P. Garcia.