Issue 18
Puzzles

Orbit crossnumber

Can you solve it?

post

6 December 2023

This guest crossnumber appeared on page 33 of Issue 18.

Download Orbit as a PDF, or read on!

Orbit, set by Kwig:

This crossnumber includes radial and clockwise clues. Half the radial entries are entered from the circumference toward the centre; the other half are entered from the centre outwards. All radial entries are four digits long except 1r, which includes the centre cell. All clockwise entries are entered clockwise. Every entry is different and none begin with zero.

Radial clues

  • 1r. The sum of this number’s digits is a cube; the product of its digits is a fourth power; and it is a multiple of 26c. (5)
  • 2r. The sum of the squares of 2c & 23c. (4)
  • 3r. A multiple of 22c. (4)
  • 4r. The length of the hypotenuse of a right-angled triangle with shorter sides 7r and 19c. (4)
  • 5r. The sum of the squares of 20c & 25c. (4)
  • 6r. A prime. (4)
  • 7r. see 4r. (4)
  • 8r. 19c + a square.$ (4)
  • 9r. 11r + a triangle number. (4)
  • 10r. The product of three distinct primes. (4)
  • 11r. The sum of four consecutive primes. (4)
  • 12r. 14r + a square. (4)
  • 13r. Another entry squared. (4)
  • 14r. 2r – a square. (4)
  • 15r. 4 more or 4 less than 16r. (4)
  • 16r. A triangle number + 23c. (4)

Clockwise clues

  • 2c. A square pyramidal number*. (2)
  • 4c. A hexagonal number**. (2)
  • 6c. The product of three distinct primes. (4)
  • 10c. 16r + 24c. (4)
  • 14c. 4c + a cube. (2)
  • 16c. A palindrome. (2)
  • 17c. A multiple of 20c. (4)
  • 18c. The sum of this number’s digit is a square. (3)
  • 19c. see 4r. (4)
  • 20c. A factor of 3r. (2)
  • 21c. 6r – a cube. (3)
  • 22c. 2c + 14c.$ (2)
  • 23c. The product of three consecutive primes. (2)
  • 24c. An anagram of 2r. (4)
  • 25c. One more than 20c. (2)
  • 26c. A square. (2)


* The $n$th square pyramidal number is the sum of the first $n$ square numbers.
** Hexagonal numbers are the number of dots in the patterns in this sequence:

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