Conqueror 3

Conqueror 3

It is recommended to view this puzzle as a document. You are also encouraged to print a physical copy. If you are unfamiliar with the rules, take a look at the first conqueror puzzle, or you can find them on the first page if viewing this puzzle as a document.


  1. There are no other entries in the whole grid that are 1 away from any of these
  2. The product ends in 7 0s
  3. Consecutive multiples of 6
  4. Sums to twice the sum at H
  5. Sums to (sum at M)*11/9
  6. The product is half a cube
  7. All end in a 1 or 2
  8. The only single digit entry in the whole grid and two multiples of it. The single digit entry is not 1
  9. All 1 away from a multiple of 5. Sums to an even number
  10. Sums to one of 109, 119 or 129
  11. When written directly next to each other in ascending order, a palindromic sequence of  digits is the result
  12. All within 10 of each other
  13. Consecutive

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Thanks to Tom and Dinos for testing this puzzle!

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All the Conqueror puzzles to date can be found here

Conquer or be Conquered

Conqueror 1

It is recommended to view this puzzle as a document. You are also encouraged to print a physical copy.


Look at the hexagonal grid below which has two types of cells – clues (black) and answers (empty). Your job is to use the clues and follow these rules to fill in all of the answers.

  • Every answer must be a whole number between 1 and 50 (inclusive) and no number appears more than once. Since there are fewer than 50 answers, not every number from 1 to 50 will appear, and the smallest and largest number that appear may not be 1 and 50 respectively.
  • Each clue is in reference to all of the answers adjacent to it, i.e. its empty neighbours. Some clues may reference other clues. When referencing a clue cell in another clue you will see it in bold underline like A
      • For example if clue A is  “Sum is 36. All prime” this means that all of the answers adjacent to clue Asum to 36 and that they are all prime numbers.
      • Then if clue B is “Sum is 2 or 3 times A” This means that the answers adjacent to clue B sum to 2 or 3 times whatever the sum of the answers adjacent to A. In this case we know this is 36, so the answers adjacent to 2 add up to either 72 or 108.

WARNING: This puzzle is difficult! To complete it you will need to be good at maths and very persistent. You will need pen and paper to write out your workings. A calculator or a computer is not necessary, and you are discouraged from using either. Knowing about prime factorisation is essential, and knowledge of modular arithmetic is helpful.


  1. All primes, and all 1 away from a multiple of 6
  2. Sum to 7 more than J
  3. Only use the digits 1 and 3
  4. The smallest and largest answer in the grid and their average. The largest is a prime
  5. Sum to a multiple of 23. All but 1 are 1 away from a square
  6. Two numbers and their sum. One of the smaller numbers is a multiple of 10
  7. Sum is twice the sum of I. Sum is 11 times greater than the smallest at G
  8. Sum is 77. No primes
  9. Product is a square which ends in 600
  10. All divisible by 3 and sum ends in 1
  11. All squares
  12. Product ends in 0. All smaller than the smallest at G
  13. Sum is a power of 2.

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New Puzzle: Let me know your score


Hop along the honeycomb from cell to cell to spell out words of length 5 or more. Each cell can only be used once in a word, and any 2 consecutive letters in the word must be adjacent in the honeycomb grid. Note that you are allowed to use the same letter twice in a word if it comes from different cells. There is definitely at least one word of every length up to 9. Each word can only be counted once even if you spot it in different places.
Take as long as you like and then score yourself as follows:

1 point for each 5 letter word

2 points for each 6

3 points for each 7

5 points for each 8

7 points for each 9+

Please remember to fill in your score here. I’ll use the data to help me set the “Average” “Good” and “Excellent” targets in future puzzles.