### Brain Teasers

# Code Breaker

Professor Abacus has scrambled the numerals 0 through 9 to form a 10-digit security code. Each numeral is used only once. Given the following clues, what is the security code?

1) The 4th and 5th digits form a triangle number.

2) The 5th and 6th digits form a prime number.

3) The 8th digit is three more than the 2nd digit.

4) The 10th digit is less than the 1st digit.

5) The sum of the 1st and 6th digits is twice the 9th digit.

6) The sum of the 3rd, 6th, and 9th digits equals 14.

7) There are three digits between the numerals 8 and 9.

8) There are no more than four digits between the numerals 1 and 4.

9) The numeral 5 is somewhere in the first five positions.

1) The 4th and 5th digits form a triangle number.

2) The 5th and 6th digits form a prime number.

3) The 8th digit is three more than the 2nd digit.

4) The 10th digit is less than the 1st digit.

5) The sum of the 1st and 6th digits is twice the 9th digit.

6) The sum of the 3rd, 6th, and 9th digits equals 14.

7) There are three digits between the numerals 8 and 9.

8) There are no more than four digits between the numerals 1 and 4.

9) The numeral 5 is somewhere in the first five positions.

### Answer

945283176028 is a triangle number, 83 is a prime number, 7 is three more than 4, 0 is less than 9, 9 + 3 is twice 6, 5 + 3 + 6 = 14, there are three digits between 8 and 9, there are four digits between 1 and 4, 5 is in the 3rd position.

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