Hello guzzlers,

I have a special treat for you today: a letter from the nineteenth century mathematician, Countess Ada Lovelace. The letter comes through the medium of Pavel Curtis, who every month for the last few years has been releasing similar puzzles from Ada that he calls Adalogical AEnigmas. Pavel, who has a day job as a software architect at Microsoft, is a legend in the puzzle community. He composed - I mean channelled - today’s puzzle for Guardian readers. Enjoy!

My dear Mr Bellos,

I should like to begin by expressing my deep gratitude for the honour you do me in presenting my little logical conundra to the readership of so august a journal as The Guardian. Truly, I am in your debt.

I am cognizant that your publication space is at a premium, so I shall, much against my accustomed nature, endeavour to be brief. In this first grid, I desire you and your readers to blacken some of the squares, in such a way as to leave all of the unblackened squares connected to one another, horizontally and/or vertically. Wherever there is a circled number, it specifies exactly how many of the squares touching it must be blackened.

The first grid: iunstructions above. To print it out, click on this link

Within this second, perhaps somewhat less genial grid, I pray that you shall enter a digit, ’twixt 1 and 7, into each and every square, refraining from placing the same digit into more than one square in any row or column. Where there exists a less-than symbol on the line separating two squares, please ensure that your entered digits obey the given inequality. Wherever a circled number has been placed, your digits must differ by precisely that amount.

The second (somewhat less genial!) grid. A printable version can be accessed using this link

When you have completed both grids, you may move on to finding the final answer to my challenge. Please begin by identifying the unblackened squares in the first grid that are in the same positions as unshaded squares in the second grid. Take the letter in each such square and advance it in the alphabet (wrapping around from Z to A if necessary) by the digit in the corresponding square. Reading the resulting letters, left-to-right and top-to-bottom, will reveal an appropriate phrase in a foreign language. Good luck! – ADA

(Click here for a printable pdf of both grids and with the instructions)

Pavel wrote his first Adalogical AEnigma in November 2013 and has since been writing them every month. They are all available for free on his website, but you can also purchase the first 24 of them as a book.

Today’s AEnigma might seem, at first glance, more difficult than the usual material in this column. Persevere! The grids are based on Japanese-style logic puzzles like Sudoku and Kakuro, and use similar deductions. However, since there are two grids, the puzzle might take you longer to solve than the puzzles I usually put up here. So rather than reveal the answer this afternoon, I will reveal it, with workings, tomorrow (Tuesday 28 March at 7am British Summer Time).

UPDATE: Read the solution here.

If you want some tips on how to start, carry on reading. Otherwise, avert your eyes and get solving!



Here’s a leg-up on how to start the first grid:

Consider the ‘3’ in the lower left corner of the grid. Since it is surrounded by three black cells, at least one of them must be *above* the three, adjacent to the ‘1’ clue. Since that *is* a ‘1’ clue up there, we can conclude that both squares below the ‘3’ (labelled ‘N’ and ‘O’) must be black. Symmetrically, since we know that one of the squares between the ‘3’ and the ‘1’ (labelled ‘G’ and ‘Q’) must be black, that’s the one black square allowed around the ‘1’, so the two squares above it (labelled ‘O’ and ‘C’) must both be white.

And here’s a start with the second grid

The only two digits that can be 6 apart are the 1 and the 7. Consider the fifth row: in which squares could a 4 appear? It can’t be in the first, fourth, or fifth column, because there aren’t any digits between 1 and 7 that are 4 or 5 away from 4. The 4 also can’t be in the second or third columns, because there aren’t four or five digits greater than 4. Finally, the 4 can’t be in the seventh column, because the only digits 3 away from 4 are 1 and 7, and those are both already spoken for in the sixth row. Therefore, the 4 in the fifth row must be in the sixth column.

OK, that’s it. See you tomorrow.

I set a puzzle here every two weeks on a Monday. Send me your email if you want me to alert you each time I post a new one.

I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

Can u solve my probs Photograph: Experiment

My puzzle book Can You Solve My Problems? is just out in the US. It is already out in the UK with a slightly different subtitle. I’m also the co-author of the children’s book Football School: Where Football Explains The World, which was a runner-up in the Blue Peter Book Awards 2017.