# Combinations and the vertical brother

When the vector product politely greeted the king,

and when the symbol of faith was with ribbon fit,

we went silent for the kill.

Hope you get the hint.

• This doesn't rhyme. Is the rhyme tag a mistake, or a hint that rhyming is involved somehow in the solution? – Rand al'Thor Jan 24 at 13:02
• Not a hint. But isn't this a rhyme? Do king,fit,kill,hint not rhyme? – George Menoutis Jan 24 at 13:18
• No. There's just assonance (same vowel each time), but not rhyme. Fill, kill, hill rhyme, and so do fit, kit, hit, but fit, kill, hint don't rhyme. – Rand al'Thor Jan 24 at 13:23
• ahh, so the consonants must be the same too. Learning something everyday. – George Menoutis Jan 24 at 13:46

Aha. The word we need is

CROSSBOW.

When the vector product politely greeted the king,


the $$\times$$ made a bow;

and when the symbol of faith was with ribbon fit,


the crucifix was tied with a bow;

we went silent for the kill.


we shot our victim with a CROSSBOW.

As for the title,

a Cartesian product (also denoted with a CROSS) involves taking all possible combinations of two or more things from given sets, and the ordinary bow could be considered a "brother" of the crossbow -- and is held vertically, unlike a crossbow. (Note: it took some prodding from OP in the comments before I understood the "vertical brother" part.)

• Correct! How about the title? – George Menoutis Jan 24 at 14:14
• Humorous, for sure :) A better title might've been rot13(Na naablrq oebgure, nf va PEBFF OEB) – Avi Jan 24 at 14:14
• I guess the combinations are a rot13(Pnegrfvna cebqhpg) but I confess I don't understand the "vertical brother" bit. – Gareth McCaughan Jan 24 at 14:19
• Correct again. The vertical brother describes the connection between the second word component and the whole word. – George Menoutis Jan 24 at 14:23

Could it be a...

permutation vector?

Explanation:

When the vector product politely greeted the king,

The king may refer to a matrix

and when the symbol of faith was with ribbon fit,

The ribbon may refer to the long square brackets for the vector notation.

we went silent for the kill.

A vector product of a matrix and a permutation vector reorders it’s rows/columns which may be perceived as twisting its structure to kill

Hope you get the hint.

Permutations and combinations are frequently discussed together in combinatorics. Hence, it could be described as its vertical brother.

• Not the intended answer. There are some math concepts in the puzzle, but not as much. – George Menoutis Jan 24 at 13:19

CROSS?

When the vector product politely greeted the king,

Vector product is also called a cross product.

and when the symbol of faith was with ribbon fit,

The symbol of the Christian faith is a cross.

we went silent for the kill.

Killing a sleeping vampire with a cross?

There might be more to it than this, though, because

I haven't explained "politely greeted the king" or "with ribbon fit". Maybe the real solution is a longer word that just starts with cross.

• Your last sentence is exactly correct! Actually, all of them except the 4th one. – George Menoutis Jan 24 at 14:05
• @George I went AFK after your comment, came back to the computer and the correct answer was posted. Fair play to Gareth. – Rand al'Thor Jan 24 at 14:35
• It was an easy one for you guys! – George Menoutis Jan 24 at 14:37