Unique, just like everyone else!
◆◆ · By SamuRai · Published 2024-06-19T05:20:07.403Z
Constructor's Note
In this puzzle there are four 2x2 squares in the corners of the larger 5x5 grid. Each cell of the 2x2s will have a single digit number. The rows and columns of the adjacent 2x2s sum to the same value which is placed in between them (using the rebus function if it is two digits). The center cell is the sum of the digits in any of the 2x2 squares (any one will do since they must all be the same). Most clues are mathematical in nature recognizing a way in which the two digit number answer is unique in some fashion. A few clues are non-mathematical bits of trivia. The summation rule will help fill the grid. Finally, much appreciation goes to @sylveon for play testing and editorial feedback.
侍 SamuRai
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1A
The smallest non-trivial palindrome in Roman numerals (i.e. not a single character like 10=X or all the same character 2=II).
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9
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14
Across
- 1AThe smallest non-trivial palindrome in Roman numerals (i.e. not a single character like 10=X or all the same character 2=II).
- 4AThe smallest number such that the prime factorization of the sum of its digits and the prime factorization of the multiplication of its digits include the first 4 primes. (for example, 15’s digits add to 6 which has prime factors 2 and 3 and multiply to 5 which has prime factors of 5. This is the smallest number that yields the first 3 primes.)
- 6AThe largest two digit decimal number with an equal number of 1s and 0s in its binary representation.
- 7ANumber that appears in many Star Trek: The Next Generation episodes. (You can blame me if you now rewatch the series looking for it!)
- 8AThe sum of entries above or below each cell.
- 9AThe smallest non-trivial decagonal number. (Number of dots that can be arranged in a 10-sided polygon, trivially 10 can do this. Similar to arranging 9 dots into a 3x3 square.)
- 11ANumber of Tetris tiles that can be made from five squares. Rotationally equivalent shapes are only counted once. (There are two that can be made from three squares and seven that can be made from four squares.)
- 13AThe smallest number with exactly ten divisors.
- 14ADistance in yards of the longest made field goal in NFL history (not math but it was a game winner against my team so I may still be bitter!)
Down
- 1DThe sum of each row, column, and diagonal for a 3x3 magic square using the digits 1 through 9.
- 2DThe smallest natural number that can be expressed as the difference of two non-zero squares in more than three ways.
- 3DThe sum of entries left or right of each cell.
- 4DThe sum of each row, column, and diagonal for a 4x4 magic square using the numbers 1 through 16.
- 5DThe smallest sum of 8 distinct prime numbers. Also the largest number of givens a sudoku can have without generating a unique solution!
- 9DIt is the largest number such that subtracting 1 from any of its divisors (except 1 and 2 but including itself) yields a prime number.
- 10DThe smallest number that can be expressed as the sum of four distinct nonzero squares in more than one way.
- 11DThe only integer that equals m^n and n^m for some unequal integers m and n.
- 12DTo be banned, in slang.