The sum of the Numbers

Can you divide numbers from 1 to 9 (1 2 3 4 5 6 7 8 9) into two groups so that the sum of the numbers of each group is equal?

Note: 9 cannot be turned over to make it 6.




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In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
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------- +
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One day, I thought of ways that can be used for creating a palindrome. So I decided that I will turn into a larger number by adding the reversed digits to the original number and keep doing it till I finally obtained a palindrome.

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If two fifty-foot ropes are suspended from a forty-foot ceiling that is twenty feet apart, how much rope will you be able to steal if you have a knife?

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There are five men, let's say Tarun Harish Lavesh, Manoj, and Manish. All of them have a dot mark on their forehead. They can't see the dots on their forehead but can see the ones on others. The owner of WHITE Dot is an honest person and will never lie, while the owner of BLACK Dot always tells the lie.

This is the statement from Tarun Harish Lavesh and Manish:
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What colour is the dot on each of Tarun Harish Lavesh, Manoj, and Manish's forehead?

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In 2007, a puzzle was released and $2 million prizes were offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found. Wiki