# Prize crossnumber, Issue 13

£100 of Maths Gear goodies to be won if you can solve it Our original prize crossnumber is featured on pages 58 and 59 of Issue 13.

### Rules

• Each clue in this crossnumber contains two statements joined by a logical connective. If the connective is AND, then both the statements are true. If the connective is NAND, then at most one of the statements is true. If the connective is OR, then at least one of the statements is true. If the connective is NOR, then neither of the statements is true. If the connective is XOR, then exactly one of the statements is true. If the connective is XNOR, then either the statements are both true or they are both false.
• Although many of the clues have multiple answers, there is only one solution to the completed crossnumber. As usual, no numbers begin with 0. Use of Python, OEIS, Wikipedia, etc. is advised for some of the clues.
• One randomly selected correct answer will win a £100 Maths Gear goody bag, including non-transitive dice, a Festival of the Spoken Nerd DVD, and much, much more. Three randomly selected runners up will win a Chalkdust T-shirt. Maths Gear is a website that sells nerdy things worldwide, with free UK shipping.
• To enter, enter the sum of the across entries below by 18 September 2021. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 1 November 2021.

### Crossnumber

Crossnumber #13, set by Humbug: ### Clues

• 1A is a multiple of 13 AND 1A is a square number.
• 1D is equal to 31A OR 1D is equal to 41A.
• 1D is prime XOR 7A is odd.
• 2D is equal to 3D OR 2D is equal to 4D.
• The sum of the digits of 3A is 27 OR the sum of the digits of 3D is 27.
• 4D is a cube number XOR 9D is a cube number.
• 4D is a square number XOR 11D is a square number.
• 5A is equal to 1A XOR 5A is equal to 3A.
• 5D is equal to 2D XOR 6D is equal to 1D.
• 7A is equal to 54A XOR 7A is equal to 12A.
• 8A is equal to 3A XOR 8A is equal to 10A.
• 10A is a factor of 3A OR 4D is a factor of 3A.
• 12A is equal to 54A XOR 12A is equal to 48A.
• The sum of the digits of 13D is 17 AND the sum of the digits of 7D is 17.
• 14A is prime NOR 14A is a multiple of a 2-digit prime.
• The sum of 15D and 16A is 742 AND the difference between 15D and 16A is 38.
• 16A is equal to 25A XOR 17D is equal to 25A.
• 16D is a multiple of 100 XOR 21A is a multiple of 100.
• The sum of the digits of 16D is 5 XOR the sum of the digits of 21A is 5.
• 17D and 15D share a factor greater than 1 XNOR 17D is the product of 1D and 48A.
• 18A is a palindrome AND 18D is a palindrome.
• The sum of the digits of 18A is 2 AND the sum of the digits of 18D is 2.
• 19D is prime XOR 27A is prime.
• 20A is prime NOR 20A is a multiple of a 2-digit prime.
• 20D is a palindrome AND the sum of the digits of 20D is 16.
• 22A is a multiple of 5 XNOR 22A is the product of 1D and 48A.
• 23A is 6 times 27A AND 28D is equal to 19D.
• 24A is a multiple of 8 AND 45D is a multiple of 24A.
• The sum of the digits of 24D is 5 XNOR the sum of the digits of 49D is 5.
• 29A is equal to 37A XOR 30D is a palindrome.
• 29A is prime XOR 37A is prime.
• 32D is a multiple of 41A AND 41D is a multiple of 41A.
• 35D is equal to 39A AND 35D is equal to 35A.
• 37D is a prime XOR the sum of the the digits of 37D is 5.
• 37D‘s first digit is 1 NAND 37D‘s last digit is 1.
• The sum of the digits of 37D is 7 XOR the sum of the digits of 30D is 7.
• 38A is a multiple of 10A AND 39A is a multiple of 10A.
• 40A is a multiple of 100 AND 45D is a multiple of 100.
• 40A is a multiple of 45D NOR 45D is a multiple of 40A.
• 40A is a square number XNOR 45D is a square number.
• 42A is a multiple of 9 XNOR 39A is a multiple of 9.
• 42A is an anagram of 33A AND 34D is an anagram of 33D.
• 43D is a multiple of 10A AND 26D is a multiple of 10A.
• 44A is equal to 5A XOR 36D is equal to 5A.
• 46A is a factor of 40A XOR 46A is a factor of 45D.
• 47D is a factor of 40A XOR 47D is a factor of 45D.
• 48A is a cube number AND 50A is a cube number.
• 48A is a square number AND 50A is a square number.
• 49D is a multiple of 5 XOR 50D is a multiple of 5.
• 52A is two more than 55A AND the sum of the digits of 52A is 3.
• 52D is a Fibonacci number AND 53D is a Fibonacci number.
• 54A is equal to 7A XOR 54A is equal to 12A.
• 54D is a Fibonacci number XOR 54D is the sum of 52D and 53D.
• 54D is a equal to 52D NOR 54D is equal to 53D.
• 56A is a square number XOR 56A is a cube number.
• 57A is a square number XOR 57A is greater than 200.