"On what did you step?" sounds silly. No one talks that way. It is acceptable, according to grammar teachers, to say, "What did you step on?"
The rule is don't use a preposition when it is not needed. That is true whether at the beginning, middle, or end of a sentence.
And remember the old joke:
A cattle buyer was seated next to an attractive woman on an airplane.
Trying to be friendly, the cattle buyer said, "Where are you from?"
With a withering look, the woman said, "From a place where we are sufficiently educated not to use a preposition at the end of a sentence."
The cattle buyer sat quietly for a few moments and then replied, "I apologize for my poor grammar. Let me rephrase my question... Where are you from, bitch?"
Adonia -- Ancient Greek Calendar
Back-to-Front Yad -- Fairy Calendar
Flitch Day (An old custom from yesteryear developed into the holiday of Flitch Day. A "flitch" of bacon was given to any married couple who could prove they had lived in harmony and fidelity for one year. Very few "took home the bacon".)
Liberation Day -- Nicaragua
Martyr's Day -- Burma
National Daiquiri Day
National Get Out of the Doghouse Day
National Hug Your Kid Day
National Raspberry Cake Day
Opet Festival -- Ancient Egyptian Festival (marriage festival)
Stick Out Your Tongue Day
St. Marcrina's Day
Isis marries Osiris (year unknown, ask the ancient Egyptians!)
Adonis marries Aphrodite (year unknown, ask the ancient Greeks!)
Stephen Anthony Lawrence, 1990
Jared Padalecki, 1982
Angela Griffin, 1976
Anthony Edwards, 1962
Brian May, 1947
Vikki Carr, 1941
Arthur Rankin, Jr., 1924
George McGovern, 1922
Robert Todd Lincoln Beckwith, 1904 (last direct descendant of Abraham Lincoln)
Max Fleischer, 1883
Charles Horace Mayo, 1865
Lizzie Borden, 1860
Edgar Degas, 1834
Samuel Colt, 1814
Today in History
A dragon more than 100 metres long was found dead on Yehwang Mountain in Henan province and was seen as a bad omen for Emperor Huan, who ignored it and died at age 35 (three years later); Xiang Kai, who had warned him of the omen, was released from the prison the emperor had placed him in, and lionised as a hero, BCE164
Moslem forces under Tariq ibn Ziyad defeated the Visigoths led by their king Roderic, 711
A hailstorm brings down the ceilings of the Papal Palace, Rome, 1500
Lady Jane Grey is replaced by Mary I of England as Queen of England after having that title for just nine days, 1553
Five women are hanged for witchcraft in Salem, Massachusetts, 1692
Australia's first recorded use of gaslight was commenced in a Sydney shop, 1826
The British Medical Association was founded as the Provincial Medical and Surgical Association by Sir Charles Hastings at a meeting in the Board Room of the Worcester Infirmary, 1832
The two day Women's Rights Convention opens in Seneca Falls, New York; "bloomers," named after developer Amelia Bloomer, are worn at this very early feminist convention, 1848