[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 278

[Sceptic Philozoff]

I don't understand it myself. The solution is very brief, the configuration of the four decks themselves is not specified. And the rules are strange, too. It follows from the solution that 12 linear quadruple decks can be placed in this 7 by 7 square. It is abnormal somehow.

[Vladimir Gomonov]

Mathemat >>:

Да я и сам не пойму. Решение очень краткое, конфигурация самих четырехпалубников не уточняется. Да и правила какие-то странные. Из решения выте4кает, что в этолм квадрате 7 на 7 можно разместить 12 линейных четырехпалубников. Ненормально это как-то.

Well, let's assume that "linear" is

****

or

*

*

*

*

and from the adjacent ones:

**

**

we have a deal?

[Sceptic Philozoff]

Come on, then. I think I'm getting the hang of it.

[Vladimir Gomonov]

Mathemat >>:

Ну давай. Кажись, в условие въехал.

Mm-hmm. I got twelve shots to guarantee a linear one (2 options. I'll draw it up now)

[Vladimir Gomonov]

			X
			X
			X
X	X	X		X	X	X
			X
			X
			X

			X
			X
		X		X
X	X				X	X
		X		X
			X
			X

[Sceptic Philozoff]

Yeah, got it.

[Vladimir Gomonov]

Mathemat >>:

Ага, понял.

I can't get it any smaller yet.

I'll get on with the squares now.

[Vladimir Gomonov]

With the square ones, one option is nine baubles.

	X		X		X
	X		X		X
	X		X		X

[Sceptic Philozoff]

In the first option, 12 is the answer.

But in the second, isn't it 9? But the answer is 20, so guess what it is.

[Vladimir Gomonov]

Mathemat >>:

В первом варианте - 12 и есть ответ.

А вот во втором - не 9 ли? Но ответ - 20. Вот и гадай, что это такое.

So the condition is misunderstood.

// Probably meant any combinations with adjacent sides, like in tetris. :)

Well, fuck it. Let's think about numbers, I mean:

Find a set of five different naturals such that any two are mutually prime, but any few numbers add up to a composite number.