problems.ru web site

• Question

  A vendor has two rolls of fabric, each `36` meters long. He sells the fabric in pieces of `3` meters. How many times will the vendor need to cut the fabric?

  Topics:

  Arithmetic Algebra -> Word Problems Logic -> Reasoning / Logic Number Theory -> Division

• Question

  A box contains `14` black socks and `14` white socks. Apart from color, all socks in the box are identical. Danny wants to take a pair of socks from the box without looking inside. How many socks does he need to take out to:

  A. Certainly have any pair of socks,

  B. Certainly have a pair of black socks?

  Topics:

  Combinatorics -> Pigeonhole Principle Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures

• Question

  Avi lives in apartment number `45`. On which floor is the apartment located if there are `2` apartments on the first floor of his building, and `4` apartments on every other floor? (Note: The building does not have a floor `0`)

  Topics:

  Algebra -> Word Problems Arithmetic -> Division with Remainder

• Question

  What is the smallest six-digit number with all different digits?

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  Topics:

  Arithmetic Proof and Example -> Constructing an Example / Counterexample

• Question

  Which of these two numbers is larger:

  `A=2011*20122012*201320132013 `  or  `B=2013*20112011*201220122012` ?

  Topics:

  Arithmetic Algebra -> Algebraic Techniques

• Question

  The number `458` is written on the board. In each single step, you are allowed to either multiply the number written on the board by `2`, or erase its last digit.

  Is it possible to obtain the number `14` using these operations?

  Topics:

  Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules Number Theory -> Division -> Parity (Even/Odd) Proof and Example -> Constructing an Example / Counterexample Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures

• Question

  Shmuel's salary increased by `20%`, and then decreased by `20%`. Is Shmuel's current salary equal to his initial salary?

  Topics:

  Algebra -> Word Problems Arithmetic -> Percentages

• Question

  The "Sweet Math" candies are sold in boxes of `12` units, and the "Geometry with Nuts" candies – in boxes of `15` units.

  What is the minimum number of boxes that must be purchased so that there are equal quantities of candies of both types?

  Topics:

  Arithmetic Algebra -> Word Problems Number Theory -> Greatest Common Divisor (GCD) and Least Common Multiple (LCM) Minimum and Maximum Problems / Optimization Problems

• Question - Movie Buffs

  Avi, Beni, and Gili love movies. Avi goes to the movies every `3` days, Beni – every `5` days, and Gili goes every `7` days. Today, they all went to the movies together. In how many days can this happen again?

  Topics:

  Arithmetic Algebra -> Word Problems Number Theory -> Greatest Common Divisor (GCD) and Least Common Multiple (LCM)

• Question

  Find five natural numbers whose sum is `20`, and whose product is `420`.

  Topics:

  Number Theory -> Division -> Parity (Even/Odd) Proof and Example -> Constructing an Example / Counterexample Number Theory -> Prime Numbers -> Prime Factorization