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## Crack the Code III

Logic puzzles require you to think. You will have to be logical in your reasoning.

 Puzzle ID: #35877 Fun: (2.46) Difficulty: (2.82) Category: Logic Submitted By: peanut

Your sister has jetted off to Europe on holiday and has left you to watch over her house and feed the cats. She is very protective over her precious cats and, hence, has a high-tech alarm system which requires a 10-digit code to deactivate it. Unfortunately, you have forgotten the code to disarm the alarm! Oddly however, you remember some mathematical facts about them...

Can you figure it out in time to feed the hungry cats?!?

* Each digit from 0 to 9 is used once only in the code.

* The sum of the numbers in the 3rd and 4th positions is equal to the product of the numbers in the 6th and 9th positions.

* The product of the numbers in the 5th and 10th positions is odd.

* The 2nd number (i.e. the number in the 2nd position) is larger than the 5th, which is larger than the 7th.

* The 8th number is larger than the 6th, which is larger than the 2nd.

* The sum of the 2nd, 6th, and 9th numbers is a perfect square.

* The sum of the 4th and 9th numbers is equal to the 10th number.

* The sum of the 1st and 5th numbers is equal to the sum of the 7th and 10th numbers.

* The number in the 9th position is even.

### Hint

The number in the 9th position is 4.
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