# math

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It is less than 100,000. it's an even number. it is divisible by 2,3, and 6. None of the digits is less than 4. None of the digits is used more than once. the sum of the digits is 30. The digit in the hundreds place is 2 less than the digit in the thousands place. The digit in the ten-thousands place is one more than the digit in the thousands place. The digit in the tens place is one less than the digit in the hundreds place. If the number were increased by 6, it would be divisible by 2,3,4,6, and 9. Find the number.

• math -

Number is abcde
a+b+c+d+e = 30
c=b-2
a=b+1
d=c-1

b+1 + b + b-2 + b-3 + e = 30
4b + e = 34
e is 4,6,8
4b = 30,28,26
so, b=7

Number is a7cd6 = 87546 = 2*3*14591
Adding 6, we get 87552 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 19

• math -

68

• math -

7

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