By Martin Gardner
A notebook of riddles, packed with enjoyable and illustrations.
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Additional info for aha! Gotcha: Paradoxes to Puzzle and Delight
A variant named "Mini Sudoku" appears in the American newspaper USA Today, which is played on a 6×6 grid with 3×2 regions. The object is the same as standard Sudoku, but the puzzle only uses the numbers 1 through 6. Another variant is the combination of Sudoku with Kakuro on a 9 × 9 grid, called Cross Sums Sudoku, in which clues are given in terms of cross sums. The clues can also be given by cryptic alphametics in which each letter represents a single digit from 0 to 9. An excellent example is NUMBER+NUMBER=KAKURO which has a unique solution 186925+186925=373850.
Often the limit takes the form of an extra "dimension"; the most common is to require the numbers in the main diagonals of the grid also to be unique. The aforementioned Number Place Challenger puzzles are all of this variant, as are the Sudoku X puzzles in the Daily Mail, which use 6×6 grids. A variant named "Mini Sudoku" appears in the American newspaper USA Today, which is played on a 6×6 grid with 3×2 regions. The object is the same as standard Sudoku, but the puzzle only uses the numbers 1 through 6.
If not only the main diagonals but also the broken diagonals sum to the magic constant, the result is a panmagic square. If raising each number to certain powers yields another magic square, the result is a bimagic, a trimagic, or, in general, a multimagic square. Different constraints Sometimes the rules for magic squares are relaxed, so that only the rows and columns but not necessarily the diagonals sum to the magic constant (this is usually called a semimagic square). In heterosquares and antimagic squares, the 2n + 2 sums must all be different.
aha! Gotcha: Paradoxes to Puzzle and Delight by Martin Gardner