.
When the multiplication 5 013 698 472 × 999 999 999 is performed,
what is the only digit that does not appear in the product?
~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let's perform the multiplication. The product is
5 013 698 472 × 999 999 999 = 5 013 698 472 × (1 000 000 000 - 1) =
= 5 013 698 472 000 000 000 - 5 013 698 472 =
5 013 698 472 000 000 000
- 5 013 698 472
--------------------------
5 013 698 466 986 301 528 <<<---=== the product
The only digit which does not appear in the product is 7.
Solved.
------------------
This problem is probably 400 or 500 years old, if not more.
It could have been created around the time the Arabs
invented the modern form of decimal notation.
It is what Britannica says
Hindu-Arabic numerals, set of 10 symbols — 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 — that represent numbers
in the decimal number system. They originated in India in the 6th or 7th century and were introduced
to Europe through the writings of Middle Eastern mathematicians, especially al-Khwarizmi and al-Kindi,
about the 12th century.
It is what AI says
The Arabs did not actually invent the modern form of numeric notation, as it originated in India
and is more accurately called the "Hindu-Arabic numeral system"; however, they were instrumental
in spreading this system to Europe, which is why they are often associated with it;
the system reached its modern form around the 8th to 9th centuries in the Arab world,
with mathematicians like al-Khwarizmi playing a key role in its dissemination.
