Logic Masters Deutschland e.V.

Are we now also on the brink of Xexit?

We‘re using them on a daily basis, be it calling, shopping or even just paying in the supermarket: The digits from 0 to 9 in our numeral system. At this year‘s Euclid congress in Alexandria, which attracts hundreds of international scientists from the mathematics scene each year, one of the digits officially announced its intended exit from the decimal system. Our editorial department for the moment has not been able to find out which digit exactly this is about. After a fierce verbal slugfest between supporters and opponents of the exit one has decided to keep the digit X a secret for now.

If, how and when the exit will happen shall be negotiated between supporters and opponents in working groups during the following weeks. Naturally, management and industry are urging a quick clarification, since in case of a Xexit even an orderly exit requires long lead times.

Meanwhile, experts are speculating about possible consequences. Because first rumors of the upcoming Xexit already gave stock market prices a good shake, effects on the global trade are being feared. On the other hand the Xexit may have a vitalizing influence on the job market, for example in mathematical research – whole branches of mathematics, number theory for instance, would have to be approached all differently.

Yet undoubtedly the biggest changes would happen to the world of puzzles. An interviewed puzzler said: "We‘re shocked, especially as in this year the World Puzzle Championship is supposed to take place in Germany for the first time in a long time. Based on the situation being so unclear we should be prepared for everything. Though the worst scenario would be this present situation in which the number X is not even known and supporters and opponents face off each other relentlessly. Our puzzle experts are currently working day and night to assess the situation‘s impact on the world of puzzles.“

By this time we received one expertise by a puzzle expert who wants to remain anonymous and said the following: "Definitely there are types of puzzles that can readily refrain from a digit. Of course the situation is totally different with other types of puzzles such as Skyscraper Sums. I have designed an example to demonstrate this.“

You can see a Skyscraper Sums with incomplete hints outside the grid, where a couple of hints is given by Xexit-supporters (shown in red in the solution) and others are given by Xexit-opponents (blue in the solution). For some hints it can not be established by which of the two groups they were given. As one can see, the Xexit-supporters completely ignore the digit X when calculating sums, and X also does not obscure any skyscrapers behind. From the hints outside the grid, the supporters completely erase the digit X, no matter whether it appears individually or as a digit in a multi-digit number. Xexit-opponents, on the other hand, treat the digit X both in the diagram and in the sums outside the grid as any other digit.

To enable also the readership to get an idea of the devastating consequences of this ambiguous situation with the Skyscraper Sums we compiled another example: