Numbers and Patterns

Number Theory Level 1

Knowing that:

9 × 9 + 7 = 88 9\times 9+7=88 ,
98 × 9 + 6 = 888 98\times9+6=888 ,
987 × 9 + 5 = 8888 987\times9+5=8888 .

What is 98765432 × 9 + 0 98765432\times9 + 0 ?

888888888 none of the above 88888888 8888888888

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Ashish Menon
May 23, 2016

The answer in each case has one 8 more than the number of digits in the extreme left being multiplied.
For example 9 × 9 + 7 \color{#D61F06}{9} × 9 + 7 has pne digit so the answer is one 8 more which is 88 88 . 98 × 9 + 7 \color{#D61F06}{98} × 9 + 7 has two digit so the answer is one 8 more which is 888 888 . 987 × 9 + 7 \color{#D61F06}{987} × 9 + 7 has three digit so the answer is one 8 more which is 8888 8888 .

98765432 × 9 + 7 \color{#D61F06}{98765432} × 9 + 7 has eight digit so the answer is one 8 more i.e. 8+1 = 9 eights which is 888888888 \color{#69047E}{\boxed{888888888}} .

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Excellent solution.

Hana Wehbi - 5 years ago

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Thanks :) :)

Ashish Menon - 5 years ago

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