Origin of going "number 1" or "number 2" in the bathroom

Solution 1:

I've deleted my other answer because A Dictionary of Slang and Unconventional English says "number one" and "number two" are from the late 1800s, citing to Joseph Manchon's 1923 Le slang: lexique de l'anglais familier et vulgaire

Also, the 1902 Slang and Its Analogues Past and Present vol. V.-N to Razzle-dazzle has:

NUMBER ONE: ...2. (nursery).- Urination; also a chamber pot

NUMBER TWO: ...2. (nursery).- Evacuation.