The Egyptian Pharaoh #2

Number Theory Level 4

$\begin{array} { l l l l l } & & A & B & C & D & E & F \\ \times & & & & & & & 4 \\ \hline & & F & E & D & C & B & A \\ \end{array}$

The pharaoh, happy after getting the answer to his previous dream thanks the users of Brilliant and then goes to sleep.

However this time again he sees another multiplication (the one above) and once again summons the Brilliant users to come and give the answer to his dream. Being a Brilliant user can you find the six-digit number $\overline{ABCDEF}$ ?

Note: In this problem, the alphabets do not need to correspond to distinct digits.

Inspired by Mohd Sasa 's The Egyptian Pharaoh .

The answer is 219978.

1 solution

Mohd Sasa
Apr 27, 2015

I really like your being inspired by the Egyptian pharaoh 1. However, I have an objection to yours. It should go like that: ABCCDE × 4 = EDCCBA That's since the number 9 is repeated twice. I'll be grateful if you accept my objection and edit the problem.

Moderator note:

It didn't specify that $C$ and $D$ must be different integers.

If that's right, then why can't the answer be 000000 ? Just an innocent question.

Mohd Sasa - 6 years, 1 month ago

It's already mentioned that $\overline{ABCDEF}$ is a 6 digit number, so $A$ and $F$ cannot be $0$ . And we did not restrict $A$ to $F$ to be all distinct numbers.

Brilliant Mathematics Staff - 6 years, 1 month ago

The Egyptian Pharaoh #2

Inspired by Mohd Sasa 's The Egyptian Pharaoh .

The answer is 219978.

1 solution

Moderator note:

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