Inspired by Pi Han Goh

Logic Level 3

1234 2345 3456 4567 5678 6789 \begin{array}{c} 1234\\2345\\3456\\4567\\5678\\6789 \end{array}

Find the odd one out from the given numbers above.

Note: Divisibility by a unique number is not a logic for solving this problem.

Inspiration .

2345 5678 6789 1234 4567 3456

Nihar Mahajan by Nihar Mahajan , 20, India

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3 solutions

Varun M
Jun 8, 2015

4567 is the only prime number among the group that is what you mean ''INSPIRATION''!!!!!

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Click on Inspiration you'll understand that!

Sravanth C. - 6 years ago
Vraj Mistry
Jun 9, 2015

3456 can also be the odd one out as it is a hamming number while others are not. Look at these links;

http://www.numberempire.com/3456

http://en.wikipedia.org/wiki/Regular_number

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Nihar Mahajan
Jun 8, 2015

Though all numbers are of form 1111 n + 123 1111n+123 , only 4567 4567 is a prime number.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

@Pi Han Goh , Can you help me in proving it? In other words we have to find solutions for a prime p p such that it satisfies the congruence:

p ≡ 123 ( m o d 1111 ) p \equiv 123 \pmod{1111}

Nihar Mahajan - 6 years ago

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By Dirichlet's theorem on arithmetic progressions , there are infinitely many primes which are congruent to 123 123 modulo 1111 1111 .

Pi Han Goh - 6 years ago

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Yeah , I realized that too. Thanks!

Nihar Mahajan - 6 years ago

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