What A Restriction!

Probability Level 1

252 , 1331 , 46764 , 9805089 252,1331,46764, 9805089

A palindrome is a number that reads the same forward as it does backwards. The above are examples of palindromes.

How many (positive) 7-digit palindromes are there?

Clarification : The leading digit of any number cannot be 0.


The answer is 9000.

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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1 solution

Rishabh Jain
Jun 17, 2016

Relevant wiki: Rule of Product - Basic

Numbers are of the form: a b c d c b a ‾ \large\overline{abcdcba} ( a , b , c , d ∈ [ 0 , 9 ] , a ≠ 0 ) (\small{\color{grey}{a,b,c,d\in[0,9]~~,a\ne 0}})

No. of ways to chose a = 9 a=9 ( Excluding 0 0 )

No. of ways to chose b = 10 b=10

No. of ways to chose c = 10 c=10

No. of ways to chose d = 10 d=10

∴ \therefore Total ways = 9 × 10 × 10 × 10 = 9000 =9\times 10\times 10\times 10=\large\boxed{\color{#007fff}{9000}}

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