1. ## Interesting one!

there are $100$ ties numbered from $1-100$. all ties numbered with a square are taken out. the remaining ties are renumbered from $1$ onwards. again all ties numbered with square numbers are taken out. the remaining tie are renumbered again $1$ onwards. find a general formula for $n^2$ number of ties for how many times square numbered ties were taken out till only a tie numbered $1$ remained

2. 100-10-9-9-8-8......-2-2-1=1 so ,18 times.

3. Hello,
Originally Posted by repcvt
100-10-9-9-8-8......-2-2-1=1 so ,18 times.
Here is a clue
1,2,3,4....100---->(10 squares are there)
1,2,3.......90---> (9 squares are there )
1,2,3.......81---->(9 squares are there)
1,2,3.......72---->(8 squares are there)
1,2,3.......64----->(8 squares are there)
1,2,3.......56----->(7 squares are there)
1,2,3.......49----->(7 squares are there)
...
....
...
....
1,2--->(1 square left)
1

watch the three steps in red
(n^2) - (n) - (n-1)= (n-1)^2
this will do
feel free to ask if trouble persists
from,