How many integers $1\le x\le2048$ such that
$$\Big\lceil \frac x{2^n}\Big\rceil$$ is not a multiple of five for all nonnegative integers $n$?
This problem is a 2020 contest problem which has finished.
Try somehow make sense of the image below. All the necessary information to solve this puzzle is there.
Good luck!
This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.
If a word conforms to a special rule, I call it a Rotting Word™.
Use the examples below to find the rule.
$$
% set Title text. (spaces around the text ARE important;...
Inspired from this question
$$
\aleph(x,n)=\lfloor x\lfloor x\lfloor x...\rfloor\rfloor\rfloor\
$$
where $\aleph$ is the inner floor function with $n$ times. For example;
$$
\aleph(x,3)=\lfloor x\lfloor x\lfloor x\rfloor\rfloor\rfloor\
$$
or
$$
\aleph(x,1)=\lfloor x\rfloor
$$
so from the pr...
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Clive James Dean Martin Lawrence
Can you do better? To make things easier, let's define a celebrity as someone who has a Wik...0
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Say my Name !!!
(Buzz, expressions of hesitance) "The United Nations, together with a European nation", repeated USA's leader, "discovered Papuan area for exotic fish" (21)
0
Lately, I've been interested in Gokigen Naname a.k.a Slalom a.k.a Slant. Luckily, Simon Tatham has a generator for Slant. Usually, the generated puzzle is so-so, but this particular generated puzzle amused me as it has a nice solving path (without guessing of course.) Then I decide to share the p...
