Sudoku is an acutely affected puzzle, and this acute to its appeal. The rules are simple to accept and the filigree – with accustomed numbers usually presented in a symmetric arrangement – is striking. Yet conceivably Sudoku is not affected enough. Conceivably the numbers on the starting filigree are an unforgivable blemish, a causeless sullying of the page.

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Or so altercate a accumulation of mathematicians, who accept appear up with a new addle genre: ‘clueless Sudoku’, which are Sudoku-style puzzles with a aboriginal starting grid. These puzzles actually don’t accept a (numerical) clue.

Below are three clueless Sudoku and an almost-clueless Killer Sudoku. Scroll bottomward for some hints and a discussion. (Click actuality for a printable area of all the grids.)

1) A 4×4 clueless Sudoku

Fill the filigree with the numbers from 1 to 4 such that no cardinal appears added than already in anniversary row or column, and that the numbers in anniversary arena add to the aforementioned sum.

(Since there are 2 regions, and the sum of all numbers in the abounding filigree is 40, anniversary arena will sum to 20.)

2) A 5×5 clueless Sudoku

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The rules are as above, but with digits from 1 to 5. (Thus anniversary arena charge sum to 15.)

3) A 6×6 clueless Sudoku

The rules are as above, but with digits from 1 to 6. (Thus anniversary arena charge sum to 14.)

4) A 6×6 about clueless Killer Sudoku

Fill in the filigree with the numbers from 1 to 6, with no cardinal actualization added than already in anniversary row, cavalcade or arena (the six-cell blocks apparent in bold). The numbers in anniversary cage (the boxes apparent by abject lines) charge sum to the absolute apparent in that cage.

Click actuality for a printable area of all the grids.

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The aboriginal three puzzles are by Gerard Butters, Frederick Henle, James Henle and Colleen McGaughey, and originally appeared in the Mathematical Intelligencer.

The fourth addle is by Philip Newman, who has afresh accomplished celebrity cachet on the band YouTube approach Cracking the Cryptic for a 9×9 about clueless Killer Sudoku, which host Simon Anthony believes “will appear to be beheld as an aberrant addle in the history of sudoku.”

Here’s an acutely absorbing blow of Simon analytic this puzzle, which explains in added detail why he believes it is such an alarming creation.

If you came actuality for the hint, actuality it is:

Hint

I’ll advice you abode the aboriginal digits in addle 3, in which every arena sums to 14. If a arena is absolutely on the aforementioned row or column, again it charge accommodate altered numbers. Attending at the leftmost column. It contains an absolute arena of three cells. The alone way to sum to 14 with three altered numbers is 6 5 3. Thus we apperceive that this arena comprises the numbers 3, 5 and 6. Now attending at the alone added three-cell region. It has one cell, apparent A, in the leftmost column, which we apperceive cannot be 3, 5 or 6. By a action of abolishment the corpuscle apparent A charge be 4. It can’t be 1 or 2, aback contrarily there aren’t ample abundant numbers that will sum to 14.

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I’ll be aback at 5pm UK with the answers. NO SPOILERS, thanks!

UPDATE: Solutions now accessible here.

Click actuality for a printable area of all the grids.

I set a addle actuality every two weeks on a Monday. I’m consistently on the look-out for abundant puzzles. If you would like to advance one, email me.

I’m the columnist of several books of puzzles, best afresh the Language Lover’s Addle Book. I additionally accord academy talks about maths and puzzles (restrictions allowing). If your academy is absorbed amuse get in touch.

Thanks to Gerard Butters, Frederick Henle, James Henle, Colleen McGaughey and Philip Newman

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