This is the eighth installment of the Fortnightly Topic Challenges Rerun described here and the forty-ninth installment of the FTCs overall, with topics suggested and voted on here. This fortnight's topic is "Pub Quiz Camouflage" (suggested by Stiv) and will span from the 7th of February to the 2...

The street outside Rockefeller Center was a very busy place to hide a secret message, I thought, but sometimes the best place to hide something was in plain sight. I'm a government agent, from one of those alphabet agencies, investigating corruption in international song competitions. I was goin...

Under 30-secs. bullet time control the above position results after nth moves. What is the fewest number of moves posible?

You are given a 5x5 square grid. Can you paint 12 cells, such that no 4 painted cells form the corners of a rectangle with sides parallel to the edges of the grid? Good luck!

Let $p$ and $q$ be a pair of twin primes. Find the smallest possible value of $a+b$ where $a$ and $b$ are positive integers such that $p\;|\;(a+qb)$ and $q\;|\;(a+pb)$. This puzzle is my own invention, a more difficult version of a problem I found elsewhere.

Suppose we have a $3\times 3$ arrangement of lightbulbs and we switch them on/off randomly (probability $½$). What is the probability the no adjacent bulbs are on? My attempt was: Let $1= $ on and $0 =$ off. Then these are the only arrangements with both no adjacent $0$s or $1$s: $$\pmatrix{ 0&1&...

Is it possible to build a gapless rectangle with non-integer side lengths using rectangles each with two integer side length and two non-integer side length? The rectangles are not required to be the same size.

I've made this up and I have no idea how easy or difficult it is. Person A has two objects B and C. A performs an experiment in her living room. She places a 100cm high solid wooden box in the centre of the room and continues as follows. A stands on the 100cm high box and holds each of the objec...

In two neigbouring cells(dimensions $1\times 1$) of square table $10\times 10$ there is hidden treasure. John needs to guess these cells. In one $\textit{move}$ he can choose some cell of the table and can get information whether there is treasure in it or not. Determine minimal number of $\texti...

An entry in Fortnightly Topic Challenge #49: Pub Quiz Camouflage After a long day at the office with little to show for it, an evening at The Badger and Biscuit (his favourite pub) was exactly what Sergeant Sequence needed to unwind. Plus, Monday night was 'KWIZ NITE' (as the owners insisted on ...

Quite simply, may White castle in the below position? There is much more than what meets the eye! Nikita M. Plaksin & Michel Caillaud, Feenschach 05/1982, 3. Prize