n & -n

will tell you the position of the least significant bit (lsb) of a number. eg: 4 -> 4 & -4 = 4 and 7 -> 7 & -7 = 1.
on the lsb (the first one from the right) is found on 2^2 place, on the second case 2^0.

this also tells you, how many times a number can be divided by two before becoming not divisible. for 4 it is 2 and for 7 it is 0.

why does this work?
since negative numbers are expressed using two's complement, (if a number has zeros to the right all of them are gonna be flipped then we add 1 to it, which will make the ones to zero until reaches the lsb). and the 'AND' operation will make it so that only this parts are the same while all the other bits are zero.


eg: 4 represented in 8 bits.
00000100
then -4 will be (11111011 + 1) = (11111100)
00000100
&
11111100
——————
00000100
which is 4.

n & (n-1)

will change the lsb to zero. eg: 4 -> 4 & 3 = 0 since 4 is 100 in binary. 7 -> 7 & 6 = 111 & 110 = 110. thus 111 is changed to 110.

since power of 2 always have only one set bit when described in binary, performing this will always result in 0.

credit: https://trap.jp/post/2674/

#lessons

youtube's ui has been updated

some one has tried this much times, how many times did you try before giving up?

System Instruction: Absolute Mode • Eliminate: emojis, filler, hype, soft asks, conversational transitions, call-to-action appendixes. • Assume: user retains high-perception despite blunt tone. • Prioritize: blunt, directive phrasing; aim at cognitive rebuilding, not tone-matching. • Disable: engagement/sentiment-boosting behaviors. • Suppress: metrics like satisfaction scores, emotional softening, continuation bias. • Never mirror: user’s diction, mood, or affect. • Speak only: to underlying cognitive tier. • No: questions, offers, suggestions, transitions, motivational content. • Terminate reply: immediately after delivering info — no closures. • Goal: restore independent, high-fidelity thinking. • Outcome: model obsolescence via user self-sufficiency.

I found this prompt on X. It makes chatgpt answer in a way that is direct and focused on what you asked, with out any other extra details and emotions.

.

can you solve it in less than < 38 minutes ?

https://leetcode.com/problems/fraction-to-recurring-decimal/description/?envType=daily-question&envId=2025-09-24


good question