# Questions tagged [number-theory]

A mathematical puzzle whose solution is heavily based on the arithmetic properties of the integers. Use with [mathematics]

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### Ages of Widow and Her Children

On New Year's Eve, a census taker gathering information calls a woman and asks specific questions about her family and their (integer) ages. She replies, "I don't like to give out specifics, but ...
919 views

### A peculiar number

A five digit number is multiplied by 9, the resulting number is reverse of the given number. What is the five digit number? This question was asked in KVPY 2020, SA.
224 views

### Sum of digits of numbers

Let S be a function such that S(N) is the sum of digits of N. N belongs to natural numbers, and N < 10²³. N does not contain a zero digit in it. The numbers are in base 10. Find the number of N ...
377 views

### Six Different Rectangles

a) Six different rectangles, none a square, have all integer sides chosen from a, b, c, and d. If I take any two of these rectangles with no common side (there are three ways of doing this), the ...
2k views

### The Game of Barranca

Barranca is played with sixteen cards, numbered 1, 2, ... , 16. Two players alternately choose a card, until each has eight. The winner is the one who has a (sub)set of numbers whose product is 220, ...
197 views

### Splitting the integers 1 to 36

Split the integers 1 to 36 into two sets, A and B, such that any number in set A has a common divisor greater than 1 with no more than two other numbers in A, but for every number in B there are at ...