Dear All, I need your help..... Please tell me how to solve these types of problems LOGICALLY..!!! QUE. Can you arrange 9 numerals - 1, 2, 3, 4, 5, 6, 7, 8 and 9 - (using each numeral just once) above and below a division line, to create a fraction equaling to 1/3 (one third)? Expecting your valuable comments......!!!!!!!

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TopNewestCongratulations on being my 300th follower! Great problem! I have no idea, however. – Finn Hulse · 3 years, 5 months ago

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5832/17496 – Vaishnav Garg · 4 years, 5 months ago

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5832/17496 – Shourya Pandey · 4 years, 5 months ago

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– Akhil K · 4 years, 5 months ago

thanks for valuable comment.Please let me know HOW you solved it.Log in to reply

– Yonatan Naamad · 4 years, 5 months ago

5823/17469Log in to reply

– Akhil K · 4 years, 5 months ago

Dear Yonatan, Please share me HOW you solved it?Log in to reply

Now I made an assumption that if I will be able to solve this problem quickly, there should be relatively few carries, If there are no carries (besides the last digit), {b,c,d} = {1,2,3}. It's easy to check that there are no solutions of this form, so we must make a weaker assumption, that there is just 1 carry. The options for {c,d} are {{1,2}, {2,3}, {1,3}}. The first pair is eliminated because e is either 1 or 2, so let's try {2,3}. ab23 = efg69. We know a+b = 1 (mod 3) and a >= 4. Now there aren't many pairs left to try, so just guess and check until we find the smallest solution of the presumed form, which is 5823. – Yonatan Naamad · 4 years, 5 months ago

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– Akhil K · 4 years, 5 months ago

congrats dear Yonatan....!!!!! This type of procedure,i had been waiting.Thanks a lot!!!!!!!!!!!!!!!!!!!!!Log in to reply