Forget base-10!

Number Theory Level 3

We all know how to count with our fingers but unfortunately we stop only at $10$ .

but if we use the base-2 to count with our fingers we can reach a highest number.

Find the biggest number we count to using base-2.

PS: the way to count is the first finger is $1$ the second is $2$ so if we want to make a $3$ w raise up the first two fingers, and so on..

1 solution

Abdeslem Smahi
Sep 11, 2015

If we raise up all the fingers we get :

$1+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9=1023$