# Arithmetic problems

New/updated : xxx

Repunits numbers with all digits = 1.
Automodular number containing its own remainder and divisor.
Power of 2 beginning by given digits.
Prepend prepending a one before a square to get a square
Derviche number The digits rotate by multiplication
Pythagorean perimeter Pythagorean triangles with given perimeter
Pythagorean square Right triangles with integer sides
Gloves Chances to pick a pair of gloves
Handshakes End of party
Resistors Resistors in parallel
Dominoes Count of tiling
Sum of squares Sum of 2, 3, 4 squares, number of decompositions
Divisors Sum of divisors, perfect and amicable numbers
Egyptian fractions The inheritance of camels
Congruent squares 3 squares in arithmetic sequence
The bookseller Equations ax+by=c
The aeronautic meeting A triangular square
The Hasting battle The big army of Harold
The Smith sisters How many sisters in Smith family, and how many socks
The pawns A rectangle or 7 squares
Coin weighings Find one or more fake coins
Fake coins II more fake coins weighings
Bags weighings Find one or more fake coins bags
The fountain Measures by pouring
The thieves Sharing a stolen barrel
Shliced numbers The first k digits build a multiple of k
The explorer Crossing the desert
Two numbers Find 2 numbers, or product of sum and product
Unrelated Shure, a usefull hint !
The ink splash Missing terms in equations
Operations Incomplete operations
Alphametic Operations with letters
Alphametic (2) Operations with letters
Digited numbers Properties of digits in a number
Digited square Properties of digits in a square
Self squared A number equals its square
Self cube A number equal to its own cube
Integer triangles Triangles with integer sides
The Smurfs How many ways of smurfing
The matches Chinese remainder theorem
The clock Angle of hands
The sandclocks Measure of time
The urn Probability of pulling 2 white marbles
Divisors  Euler´s totient and square free divisor
Latins Latin and graeco-latin squares