 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 7Digit Number
 Work out the largest 7digit 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.
