Issue 20
Crossnumber

Prize crossnumber, Issue 20

Can you solve it?

post

8 November 2024

Our original prize crossnumber is featured on pages 70 and 71 of Issue 19.

Rules

  • In the completed crossnumber:
    • The number of entries that are even numbers is an even number;
    • The number of entries that are odd numbers is an odd number;
    • The number of entries that are prime numbers is a prime number;
    • The number of entries that are square numbers is a square number;
    • The number of entries that are multiples of 3 is a multiple of 3.
  • There is only one solution to the completed crossnumber. Solvers may wish to use the OEIS, Python, their ZX Spectrum, etc to (for example) obtain a list of prime numbers, but no programming should be necessary to solve the puzzle. As usual, no entries begin with 0.
  • 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, submit the sum of all the digits in the row marked by arrows using this form by 14 April 2025. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 1 June 2025.

Crossnumber

Crossnumber #20, set by Humbug:

Across clues

  • 1. A factor of 9999. (4)
  • 4. A multiple of 32. (4)
  • 7. 22 more than 22A. (3)
  • 9. Each digit of this number (except this first) is either equal to or one less than the previous digit. (5)
  • 11. 22 more than 42A. (3)
  • 13. A multiple of 201. (4)
  • 15. The sum of this number’s digits is 13. (4)
  • 17. Less than 33. (2)
  • 18. Two times 44A. (7)
  • 21. Six less than 47A. (2)
  • 22. 22 more than 56A. (3)
  • 24. 111 more than 40A. (3)
  • 25. An anagram of two times 27D. (3)
  • 27. Two times 29A. (6)
  • 29. Two times 36A. (6)
  • 32. 34 more than a multiple of 100. (5)
  • 33. Two times 27A. (6)
  • 36. Two times 32A. (6)
  • 39. A multiple of 9. (3)
  • 40. A multiple of 111. (3)
  • 42. 22 more than 7A. (3)
  • 43. 30 less than a factor of 34D. (2)
  • 44. Two times 33A. (7)
  • 47. Six more than 21A. (2)
  • 48. A multiple of 1. (4)
  • 50. A multiple of 39. (4)
  • 52. 36 times 3D. (3)
  • 53. Each digit of this number (except this first) is either equal to or one less than the previous digit. (5)
  • 56. A multiple of 50. (3)
  • 57. A multiple of 1000. (4)
  • 58. One more than 57A. (4)

Down clues

  • 1. The product of the digits of 28D. (3)
  • 2. A multiple of 201. (4)
  • 3. The sum of the digits of 28D. (2)
  • 4. A square number. (2)
  • 5. The sum of this number’s digits is 12. (4)
  • 6. 22 more than 11A. (3)
  • 8. A multiple of 203. (5)
  • 10. A multiple of 9. (4)
  • 12. A multiple of 9. (5)
  • 14. Each digit of this number (except this first) is either equal to or one less than the previous digit. (4)
  • 16. A multiple of 3. (4)
  • 19. A multiple of 10. (7)
  • 20. A multiple of 10. (7)
  • 23. A multiple of 1001. (5)
  • 26. A multiple of 9. (5)
  • 27. An anagram of five times 25A. (3)
  • 28. A multiple of 2. (3)
  • 30. A multiple of 1. (3)
  • 31. An anagram of 468. (3)
  • 34. An anagram of 56789. (5)
  • 35. A multiple of 5. (4)
  • 37. A multiple of 5. (4)
  • 38. A multiple of 601. (5)
  • 41. A multiple of 1111. (4)
  • 45. A multiple of 302. (4)
  • 46. One of this number’s digits is 1. (4)
  • 49. Less than 333. (3)
  • 51. The sum of this number’s digits is 4. (3)
  • 54. A multiple of 10. (2)
  • 55. Three more than 54D. (2)

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