When you hear the common Italian expression metterci una croce sopra (to put a cross on it) you might very likely think of a cross in a cemetery, and that would make sense. You are closing the door on something, burying it, so it's dead to you, you're putting it behind you. But a little research tells us that the origin of the expression is something else entirely.
But first, let's mention a couple of variants of the expression. Many or most expressions change over time or according to region, and this one is no exception. In the following example, the verb fare (to make) is used in place of mettere (to put), but the substance doesn't change.
Per quanto riguarda Parigi, meglio... meglio farci una croce sopra.
Regarding Paris, it's better... it's better to make a cross on it [to cross it off].
Captions 21-22, Volare - La grande storia di Domenico Modugno Ep. 1 - Part 29
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And here, too, it can be fare una croce sopra or farci una croce sopra. The ci stands for "on it" and reinforces the preposition sopra (on / on top of). And in English, we can cross something off a list, or we can cross something out, by putting an X on it, for example. In other words, we use the verb "to cross out" or "to cross off," or we can mark something with an X. But we don't use the noun "cross" for this.
We visited this Italian language website for more information and learned that, although many people do think of a cross in a cemetery when hearing the above-mentioned expression, it actually comes from the field of ragioneria or accounting. In earlier times, before spreadsheets, when it seemed very unlikely that a client would pay up, the accountant would put an X in the margin to call attention to the fact that this money would never be recovered. So when you put an X next to something, you know it is futile, so you just put it behind you.
The cemetery image is not irrelevant however because, interestingly, there is another, very similar expression in Italian, which does have to do with gravestones and cemeteries. The meaning is almost identical, at least nowadays. Una pietra is "a stone," and here it refers to a tombstone or gravestone.
Quindi, perché non ci mettiamo una bella pietra sopra e ripartiamo da zero, eh?
So, why don't we put it behind us and start over from scratch, huh?
Caption 75, Il Commissario Manara S1EP5 - Il Raggio Verde - Part 2
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Vabbè, su quella ormai ci ho messo una pietra sopra.
OK, I've already turned the page on that by now.
Caption 50, Sposami EP 3 - Part 7
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Some graves have crosses, some graves have stones, and some have both. As we see in the translations, there are various ways to say the same thing, depending on the context.
When talking about the old year that just ended, some of us might want to put a cross or tombstone on it. Others might have had a great year! Whatever kind of year you had in 2023, we hope 2024 brings happiness and all things good!