Hopefully this will form the first question of a sequence of questions from $\mathtt{Densa^{TM}}$
Here goes, which is the odd one out?
And this question DOES have an answer!
The left and right numbers are linked. What should the last number on the right be, and why?
\begin{align}
135759&: 1 \\
151364&: 4 \\
255075&: 9 \\
279422&: 36 \\
292620&: 91 \\
348777&: 135 \\
398067&: 147 \\
417894&: 265 \\
459431&: 279 \\
478926&: 307 \\
609941&: 363 \\
689245&: 435 \\
814576&...
Calculate the determinant of the matrix
$$
\begin{pmatrix}
10^{10} & 10^{10^{10}} & 11^{11^{11}} & 1 & 0 \\
2^{2^2} & 3^{3^3} & 7^{7^7} & 0 & 1 \\
11 & 17 & 12 & 2 & 7 \\
2 & 3 & 5 & 1 & 1 \\
9 & 14 & 7 & 1 & 6 \\
\end{pmatrix}
$$
My wonderful Russian Professor put this one up ...
Start at the mountain of kings
Then go down the country to face the oldest rivals.
Go on down through the bizarre,
And you'll find the place that cuts.
Go south to find birds,
Then leave to see those who fought metal in the end.
Go North, passing the one above
To end where the lightning strikes.
...
These apples have no nutritional value. Why?
I'll just state some sudoku solving strategies in general, so not for the sudoku posted by you in particular. (NOTE: You probably know the first few, but I just state all of them for completeness.)
1. Naked Single
Probably the easiest one that everyone knows: When there is only one candidate av...
