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Number Theory Level 1

111 , 111 , 111 × 111 , 111 , 111 = ? \large{111,111,111 \times 111,111,111 =}\, ?


The answer is 12345678987654321.

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Rishabh Sood by Rishabh Sood , 20, India

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1 solution

11 ⏟ 2 digits × 11 = 1 21 111 ⏟ 3 digits × 111 = 12 321 1111 ⏟ 4 digits × 1111 = 123 4321 11 , 111 ⏟ 5 digits × 11 , 111 = 1234 54321 ⋮ 111 , 111 , 111 ⏟ 9 digits × 111 , 111 , 111 = 12345678 987654321 \begin{aligned} \underbrace{11}_{\color{#D61F06}{2}\; \text{digits}}& \times\; 11=1\color{#D61F06}{2}1\\ \underbrace{111}_{\color{#D61F06}{3}\; \text{digits}}& \times\; 111=12\color{#D61F06}{3}21\\ \underbrace{1111}_{\color{#D61F06}{4}\; \text{digits}}& \times\; 1111=123\color{#D61F06}{4}321\\ \underbrace{11,111}_{\color{#D61F06}{5}\; \text{digits}}& \times\; 11,111=1234\color{#D61F06}{5}4321\\ \vdots \\ \underbrace{111,111,111}_{\color{#D61F06}{9}\; \text{digits}}& \times\; 111,111,111=\boxed{12345678\color{#D61F06}{9}87654321} \end{aligned}

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Thank you for posting a solution

Rishabh Sood - 4 years, 12 months ago

Yeah I did the same

John Green - 4 years, 11 months ago

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