Absolute Values, Oh My!

Relevant wiki: Absolute Value Problem Solving - Intermediate

$1+2+...+62=1953<2010 \implies || \cdots ||2010-1|-2|-3|-\cdots -62|=57$

Then

$||57-63|-64|=57+64-63=58$ and so on (it gets bigger by one each time)

we get: $|||\cdots |||2010-1|-2|-3|-\cdots -99|-100|=57+(64-63)+\cdots +(100-99)=57+1+1+\cdots +1=57+19\cdot1=76$

So $x=76$

(note that from 63 to 100 is 38 numbers. since it take 2 of them to make a result 1 there is 19 such results)

Solve the modulus up to 62 @ because 62 is last +ve After that our question makes an ap then solve it