Did you solve it? The queens of chess

Earlier today I set you the following chess-themed conundrums:

1. The quintet of queens.

The answer is 3, and the only possible arrangement of the queens (except for rotations and reflections) is as below. The blue dots show the squares not being attacked.

2. Four king hell.

Here’s the answer:

How might you have deduced this? Well, you know that each ‘kingdom’, or segment must contain 16 squares. And you might have asked: what kind of 16-square segment would fit together with three identical segments to make am 8x8 square? I mentioned that orientations were different, so it would be most likely that they are, relative to each other, in the four compass directions. I also mentioned that each piece touches a side of the board. With a flash of insight, you may have envisioned the ‘spiral’ form.

3. Magyar o’clock.

Below are four time expressions in Hungarian, followed by their expression in numerals.

Három perc múlva háromnegyed három: 2.42

Három perccel múlt háromnegyed három: 2.48

Négy perc múlva negyed három: 2.11

Négy perccel múlt négy: 4.04

How would a Hungarian say 3.03 and 3.19?

The solutions are:

3.03 Három perccel múlt három

3.19: Négy perccel múlt negyed négy

Here’s how I worked it out. The final line suggests that négy is 4. Perc(cel) appears in the same position in all of them so is probably hours or minutes, and so múlt is probably ‘past’.

The confusing word in the other lines is három, which appears three times in the first two sentences and once in the third. In fact, the first two sentences differ only in that one has perc múlva and the other has perccel múlt, which we have hypothesised might be ‘minutes past’. So perc múlva might be ‘minutes to.’

How might 2.48 and 2.42 be related if one is the same number of minutes more and the other one is the same number of minutes less? Well, it works counting three minutes backwards or forwards from 2.45. Let’s say, therefore, that három is 3. Then háromnegyed három must be 2.45. How? Well, again we have seen that négy is 4, so this might suggest that negyed is ¼, which means that the Hungarian phrase for 2.45 is ‘three quarters [on the way to] three]. In other words, when mentioning quarter-hours Hungarians refer to the hour that is coming rather than the hour that has just past. Thus négy perc múlva negyed három is ‘four minutes to a quarter [on the way to] three’, or 2.11.

We can now deduce that:

3.03 is három perccel múlt három. (Three minutes past three)

3.19 is négy perccel múlt negyed négy. (Four minutes past a quarter [hour] [on the way to) four.)

I hoped you enjoyed these puzzles. I’ll be back in two weeks.

If you enjoyed the Hungarian one, you may enjoy my latest book, The Language Lover’s Puzzle Book, which contains many similar puzzles, in many different languages.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

Thanks to Mathigon for the first two puzzles. Mathigon is a brilliant, free educational website whose annual online puzzle advent calendar begins tomorrow on this link. The site is an incredible resource, simple to use and navigate, beautifully designed, and full of amazing maths. Go visit!