Prize crossnumber, Issue 12

£100 of MathsGear goodies to be won if you can solve it

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Our original prize crossnumber is featured on pages 56 and 57 of Issue 12.

Rules

  • 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 clues below by 3 September 2020. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 1 October 2020.

Crossnumber

Crossnumber #12, set by Humbug:

Clues

Across

  • 1 3 times 2D. (3)
  • 3 3 times a palindrome. (3)
  • 5 3 more than 33A. (3)
  • 7 3 times the reverse of 11A. (3)
  • 9 3 less than 2D. (3)
  • 10 3A backwards. (3)
  • 11 3 times the reverse of 18A. (3)
  • 12 3 more than a prime. (3)
  • 14 3 more than an even number. (3)
  • 16 3 more than a multiple of 10. (3)
  • 18 3 times the reverse of 8D. (3)
  • 20 3 more than 31A. (3)
  • 22 3 more than 15D. (3)
  • 24 3 more than a multiple of 110. (3)
  • 26 3 times 67A. (3)
  • 28 3 copies of the same digit. (3)
  • 29 3 less than 57D. (3)
  • 30 3 times 16A. (3)
  • 31 3 less than 20D. (3)
  • 33 3 times 57D. (3)
  • 35 33 more than a multiple of 100. (3)
  • 37 3 times 17D. (3)
  • 39 3 digit integer. (3)
  • 41 3 times a prime. (3)
  • 43 33 is the highest common factor of 43D and this number. (3)
  • 45 3 less than 46D. (3)
  • 47 33 is the highest common factor of this number and 63D. (3)
  • 48 3D backwards. (3)
  • 49 3 copies of the same digit. (3)
  • 50 300 more than 39A. (3)
  • 52 31 times a prime. (3)
  • 54 33 is the highest common factor of 44D and this number. (3)
  • 56 3 more than a square. (3)
  • 58 3 times a prime. (3)
  • 60 3 copies of the same digit. (3)
  • 62 3 less than an even number. (3)
  • 64 3 times a square. (3)
  • 66 3 is the product of this number’s digits. (3)
  • 67 3 times a multiple of 5. (3)
  • 68 3, 6 and 9 are the three digits of this number. (3)
  • 69 3 times the product of 58D’s digits. (3)
  • 70 3 copies of the same digit. (3)
  • 71 3 times 63D. (3)
  • 72 3 less than 64A. (3)

Down

  • 1 3 times 12A. (3)
  • 2 3 more than 9A. (3)
  • 3 3 less than an even number. (3)
  • 4 3A backwards. (3)
  • 5 3 more than an even number. (3)
  • 6 3 more than a multiple of 10. (3)
  • 7 3 less than 38D. (3)
  • 8 3 more than an odd number. (3)
  • 13 31 more than 62D. (3)
  • 15 3 times this number is even. (3)
  • 17 3 is the product of this number’s digits. (3)
  • 19 300 more than 7A. (3)
  • 20 3 more than 21D. (3)
  • 21 3 less than 20A. (3)
  • 22 3 more than 28A. (3)
  • 23 3 more than the sum of this number’s digits is 20. (3)
  • 24 3 less than a multiple of 112. (3)
  • 25 33 less than a multiple of 122. (3)
  • 26 3 times 34D. (3)
  • 27 3 times 6D. (3)
  • 32 3 times 31A. (3)
  • 34 3 more than a multiple of 4. (3)
  • 36 3, 6 and 9 are the three digits of this number. (3)
  • 38 3 less than a palindrome. (3)
  • 39 3 more than 39A. (3)
  • 40 30 more than 39A. (3)
  • 41 33 times a prime. (3)
  • 42 37 times a prime. (3)
  • 43 33 is the highest common factor of 54A and this number. (3)
  • 44 33 is the highest common factor of 43A and this number. (3)
  • 45 3 less than 56A. (3)
  • 46 3 more than a prime. (3)
  • 51 3 times 39D. (3)
  • 53 3, 6 and 9 are the three digits of this number. (3)
  • 55 3 copies of the same digit. (3)
  • 57 3 more than 29A. (3)
  • 58 3 odd digits. (3)
  • 59 3 times the product of 69A’s digits. (3)
  • 60 3 copies of the same digit. (3)
  • 61 3 copies of the same digit. (3)
  • 62 3 more than 62A. (3)
  • 63 3 times a multiple of 11. (3)
  • 64 333 times a square. (3)
  • 65 3 times a square. (3)

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