# Prize crossnumber, Issue 19

Can you solve it?

Our original prize crossnumber is featured on pages 64 and 65 of Issue 19.

### Rules

• In this crossnumber, each clue is satisfied by both the entry and the reverse of the entry. For example, if the clue for a 4-digit entry is `multiple of 5′ then the entry could be (for example) 5105 or 5225 (as these numbers reversed are 5015 and 5225 which are also multiples of 5), but it could not be 4125 (as this number reversed is 5214 which is not a multiple of 5).
• There is only one solution to the completed crossnumber. Solvers may wish to use the OEIS, Python, a graphical calculator, etc to (for example) obtain a list of cube numbers, but no programming should be necessary to solve the puzzle. No entries end with 0. 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 8 October 2024. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 1 November 2024.

### Crossnumber

Crossnumber #19, set by Humbug:

### Across clues

• 1. A prime number. (2)
• 3. A multiple of 3. (2)
• 5. Less than 30. (2)
• 7. An even number. (3)
• 10. A factor of 270. (2)
• 11. Not a multiple of 3. (5)
• 13. A multiple of 3. (3)
• 14. A multiple of 8. (4)
• 16. The sum of the digits of 12D. (2)
• 17. A multiple of 3. (2)
• 18. Equal to 3D. (10)
• 23. Greater than 90. (2)
• 25. A multiple of 6. (2)
• 26. A multiple of 3 and not a multiple of 9. (3)
• 27. The sum of the digits of 7A. (2)
• 28. Less than 1170000. (7)
• 31. Each digit of this number (except the first and last) is the mean of the digits either side of it. (3)
• 33. Less than 222. (3)
• 34. Greater than 2222222. (7)
• 37. One more than a prime number. (2)
• 38. Greater than 380. (3)
• 40. A factor of 132. (2)
• 41. Not a prime number. (2)
• 42. The sum of this number’s digits is 14. (10)
• 46. Not a prime number. (2)
• 47. A multiple of 9. (2)
• 48. Less than 1234. (4)
• 51. A multiple of 52D. (3)
• 53. Less than 66666. (5)
• 55. Greater than 90. (2)
• 56. A multiple of 51D. (3)
• 57. A prime number. (2)
• 58. A factor of 84. (2)
• 59. Less than 37A. (2)

### Down clues

• 1. A square number. (3)
• 2. A multiple of 11. (3)
• 3. Equal to 18A. (10)
• 4. The sum of the digits of 11A. (2)
• 5. Less than 2222222. (7)
• 6. The sum of the digits of 3D. (2)
• 7. A multiple of 8. (4)
• 8. Equal to 59A. (2)
• 9. A multiple of 4. (2)
• 12. An odd number. (3)
• 15. A prime number. (2)
• 17. The sum of this number’s digits is 10. (10)
• 19. Greater than 600. (3)
• 20. A multiple of 3 and not a multiple of 9. (2)
• 21. Equal to 21D. (5)
• 22. Not a multiple of 5. (2)
• 23. Not equal to the sum of the digits of 28A. (2)
• 24. An odd number. (5)
• 29. The sum of this number’s digits is 17. (2)
• 30. Each digit of this number (except the first and last) is the mean of the digits either side of it. (7)
• 32. The sum of the digits of 5D. (2)
• 35. Less than 300. (3)
• 36. The sum of this number’s digits is 5. (2)
• 37. One less than a prime number. (2)
• 39. An odd number. (2)
• 43. A multiple of 1111. (4)
• 44. Less than 222. (3)
• 45. Not a prime number. (2)
• 49. Not equal to 50D. (3)
• 50. Not a multiple of 3. (3)
• 51. A prime number. (2)
• 52. Not a prime number. (2)
• 53. A multiple of 9. (2)
• 54. A factor of 1612. (2)

• ### Read Issue 19 now!

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