1234567890....
This shows easily which kinda Gate is useful for your purposes.
You got all gates there and you can switch through all pin combinations.
It tells you exactly at what digit it will stop counting...
1) Have all switches off first.
2) Choose any A B C D combination using the 8 switches on the right.
3) choose the gate you want to test on its count behavior
4) turn the Impuls switch on coming from the 555 output on 3
ENJOY