Our original prize crossnumber is featured on pages 58 and 59 of Issue 13.

- Download Crossnumber #13 as a PDF, or read on!
- Submit your answer

### 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.