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Three write-ups on the small questions behind these tools: how an exact age is counted when months are different lengths, what makes a prize draw genuinely fair rather than merely random-looking, and how to read the Roman numeral on a building without counting on your fingers.

Where to start

How to pick a random winner fairly is the most useful of the three, and the least obvious. Fairness in a draw has two separate requirements, and most people only think about one of them: the randomness has to be sound, and the process has to be something the people who did not win can believe afterwards.

What these pieces have in common

These are the questions that come up outside work, where the stakes are low enough that nobody researches them and the usual answer turns out to be slightly wrong. Calculating an exact age is arithmetic that everyone assumes they can do and that drifts by days when done the obvious way. Reading Roman numerals is a system most people half remember, which is enough for a clock face and not for a copyright date.

It is a small category and it will grow slowly, because the bar for adding something here is that the question genuinely comes up and the common answer is genuinely off.

Frequently asked questions

How do you run a prize draw that people will accept as fair?

Decide the rules before you see the entries, use a source of randomness that is not a human choice, and make the process observable, by recording the draw or by using a method others can repeat. A result nobody can check is treated as suspect no matter how fairly it was produced.

What is the rule for subtraction in Roman numerals?

Only I, X and C subtract, and each only from the next two higher symbols: IV and IX, XL and XC, CD and CM. That is why 1999 is MCMXCIX and not MIM. A symbol is never subtracted from one more than two steps above it.

Why does dividing days by 365.25 give the wrong age?

Because it averages away the structure of the calendar. Months have different lengths and leap years fall on an irregular pattern, so the average is right across centuries and wrong for one person. Counting whole years to the last birthday and then the remainder gives the exact figure.

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