Solution needed for counting pulse inputs WITHOUT using Intterupts

You can set the timers of an Arduino to external clock signal, and use them to count your pulses.

Timer1 and Timer2 are best for this (Timer0 is used by the millis() function and other Arduino specific functions, so don't use that timer if you want to use milis()). Note that both timer0 and timer2 are 8-bit so roll over at 256, timer1 is 16-bit rolling over at 65536.