Can you paint $7$ cells of a $7 \times 7$ grid such that the Euclidean distance* between any pair of painted cells is distinct? Good luck!
*The Euclidean distance between cells $(r_1,c_1)$ and $(r_2,c_2)$ is $\sqrt{(r_1-r_2)^2+(c_1-c_2)^2}$.
A is the son of P and brother in law of T, who is the sister of G. B is the husband of K. K has only two children, T is one of them. S is the mother of A and sister of W who is the husband of R. U is the brother of P.
If V is the brother of A, then who is the aunt of V? It would be great if som...
The words on the page
Arranged in neat lines
Like a play on a stage
When done well - there I shine.
On joyful, bright days
And downcast, sad ones too
When you meet someone's gaze
I'll be there, clear and true.
Anger burns and flares out
And I'm there in the hurt
If you yell , scream, and shout
I...
Let $f : \mathbb{N} \rightarrow \mathbb{N}$ be a function satisfying $y < f(x+1) \rightarrow y < f(x)$ for every $x, y \in \mathbb{N}$. Show that this function is bounded and determine the bound.
Steal my prefix and fire shall arise.
Steal my suffix and someone dies.
Steal my infix and differ from guys.
Steal my whole and go reorganize.
