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Remainder/Divisibility Puzzles

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Remainder/Divisibility Puzzles, a selection of answers from the Dr. Math archives.

Remainders of 1, 2, 3, 4
Find the smallest whole number that when divided by 5, 7, 9, and 11 gives remainders of 1, 2, 3, and 4 respectively.

Remainder Problem
What number less than 500 produces remainder 4 when divided by 5, remainder 7 when divided by 9, and remainder 9 when divided by 11?

Multiply Two Numbers (No Zeros) to make 5 Billion
What two numbers, neither of them containing zeros, can be multiplied together to make 5,000,000,000?

One Billion as Product of Two Numbers with No Zeros
Write 1,000,000,000 as the product of two numbers, neither of which contains any zeros.

Sums Divisible by 11
Why is the sum of a number with an even number of digits and that same number written in reverse always divisible by 11?

Largest 7-Digit Number
Work out the largest 7-digit number you can applying two rules: every digit in the number must be able to be divided into the number, and no digit can be repeated.

Extraordinary Social Security Number
The number's nine digits contain all the digits from 1 to 9. When read from left to right the first two digits form a number divisible by two, the first three digits form a number divisible by three...

Divisibility Word Problem
Arrange the digits 0 to 9 such that the number formed by the first digit is divisible by 1, the number formed by the first two digits is divisible by 2, that formed by the first three digits divisible by 3, and so forth; thus the number formed by the first 9 digits will be divisible by 9 and that formed by all 10 digits divisible by 10.

Find the Smallest Number - A Remainder Problem
Find the smallest number, M, such that: M/10 leaves a remainder of 9; M/9 leaves a remainder of 8; M/8 leaves 7; M/7 leaves 6; M/6 leaves 5; M/5 leaves 4; M/4 leaves 3; M/3 leaves 2; and M/2 leaves 1.

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