Patterns in Numbers and Digits
Problems on periodicity. Spot patterns in them!
JuniorMathematics
Arithmetic · Patterns in Numbers and Digits
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Interactive puzzles
7 puzzles in this collection
A. Decimal expansions and repeating fractions Verify these decimal expansions:
Show that any purely periodic proper fraction equals a fraction whose numerator
is divisible by 7, prove that it is also divisible by 11, 13, and 15,873. In the
If this digit is moved to the front, the number doubles. Find the smallest such
Prove that any cyclic permutation of its digits is also divisible by
Problems on periodicity.
Learn the methodRead guide
Problems on periodicity.
Spot patterns!
All puzzles
All puzzles
A. Decimal expansions and repeating fractions Verify these decimal expansions:
Show that any purely periodic proper fraction equals a fraction whose numerator
is divisible by 7, prove that it is also divisible by 11, 13, and 15,873. In the
If this digit is moved to the front, the number doubles. Find the smallest such
Prove that any cyclic permutation of its digits is also divisible by
Example: knowing that 93,767 is divisible by 41, conclude that 37,679 is divisib
D. Base‑16 (hexadecimal) curiosities Does there exist a hexadecimal number that,