Sudoku is an extremely beautiful puzzle, and that’s what accounts for its appeal. The rules are easy to understand and the grid – with the numbers given, usually presented in a symmetrical pattern – is striking. Yet perhaps Sudoku isn’t elegant enough. Perhaps the numbers on the starting grid are an unforgivable flaw, an unnecessary slander of the page.
Or argue with a group of mathematicians who have come up with a new puzzle genre: ‘clueless sudoku’, which are Sudoku-style puzzles with an ancient starting grid. These puzzles have literally no (numerical) clues.
Below are the three Unknown Sudoku and the Almost Unknown Killer Sudoku. Scroll down for some hints and discussion. (Click here for a printable sheet of all grids.)
1) A 4×4 Unknown Sudoku
Fill the grid with numbers from 1 to 4 such that no number appears more than once in each row or column, and the numbers in each field add up to the same sum.
(Since there are 2 regions, and the sum of all the numbers in the complete grid is 40, the sum of each region will be 20.)
2) a 5×5 uncanny sudoku
The rules are given above, but with numbers from 1 to 5 (thus the sum of each field should be 15.)
3) A 6×6 Unknown Sudoku
The rules are as above, but with numbers from 1 to 6 (thus the sum of each field should be 14.)
4) A 6×6 Almost Unknown Killer Sudoku
Fill the grid with numbers from 1 to 6, with no numbers appearing more than once in each row, column, or region (six-cell blocks marked in bold). The number in each cage (boxes marked by dashed lines) should be equal to the sum of the total marked in that cage.
Click here for a printable sheet of all grids.
The first three puzzles are by Gerard Butters, Frederick Hale, James Henley and Colleen McGaughey, and originally appeared in mathematical intelligence.
The fourth puzzle is that of Philip Newman, who recently achieved celebrity status on the cult YouTube channel cracking the cryptic The nearly unknown killer Sudoku for a 9×9, which host Simon Anthony believes “will be seen as an extraordinary puzzle in the history of Sudoku.”
Here’s an extremely entertaining clip of Simon solving this puzzle, which goes into more detail why he considers it such an amazing creation.
If you came here for the hint, it is it:
Signal
I’ll help you place the first digit in Riddle 3, in which the sum of each field is 14. If a field is entirely on the same row or column, it must contain different numbers. Look at the leftmost column. It consists of a whole area of three cells. The only way to sum 14 with three different numbers is 6 + 5 + 3. Thus we know that this field consists of the numbers 3, 5 and 6. Now let’s just look at the other three-cell area. It has a cell, marked A in the leftmost column, which we know cannot be 3, 5 or 6. The cell marked A should be 4 by the process of elimination. It cannot be 1 or 2, otherwise there are not large numbers whose sum is 14.
I will be back in the UK at 5 pm with a reply. No spoilers, thanks!
Click here for a printable sheet of all grids.
I set a puzzle here on Mondays every two weeks. I am always on the lookout for great puzzles. If you want to make a suggestion, e mail me.
I’ve been the author of several puzzle books lately Language lover’s puzzle book. I also give school talks about math and puzzles (restrictions allowed). If your school is interested please keep in touch
Thanks to Gerard Butters, Frederick Hale, James Henley, Colleen McGaughey and Philip Newman