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The Divided Secret Puzzle - Solution
The Puzzle:
When you divide a certain number by 3, the remainder is 1.
When you divide the same number by 5, the remainder is 2.
When you divide it by 7, the remainder is 3.
What is the smallest positive number that satisfies these conditions?
Our Solution:
52
Method:
Begin by putting the clues into linear form:
x = 3k + 1
x = 5m + 2
x = 7n + 3
k, m and n are integers
Equate first 2 equations: 3k + 1 = 5m + 2
So: k = (5m+1)/3
At this point we can continue solving, or do trial and error:
m=1, k = 6/3 = 2
m=2, k = 11/3 = not a whole number
m=3, etc
m=4, etc
...
m=10, k = 51/3 = 17
We can test all m values where k is a whole number, and on testing m=10, k=17 we get:
x = 3x17 + 1 = 52
x = 5x10 + 2 = 52
x = 7x7 + 3 = 52
Solved!
Puzzle Author: Pierce, Rod