Half Filled barrel

We have shown you a regular water barrel as below. Without using any measuring device can you check if the barrel is more than half-filled or less than half-filled?

Half Filled barrel




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When I divide it by 3, the remainder is 2.
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When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

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Amazing Facts

Word ladder puzzle

The word ladder puzzle was invented by Lewis Carroll, author of Alice’s Adventures in Wonderland.