Arithmetic

Arithmetic is the fundamental branch of mathematics dealing with numbers and the basic operations: addition, subtraction, multiplication, and division. Questions involve performing these operations, understanding number properties (like integers, fractions, decimals), and solving related word problems.

• The Number

  Given a positive integer less than 2000.
  If it is not divisible by 43, then it is divisible by 41,
  If it is not divisible by 53, then it is divisible by 43,
  If it is not divisible by 41, then it is divisible by 53.
  Find the number.

  Topics:

  Number Theory -> Prime Numbers Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules Logic -> Reasoning / Logic Number Theory -> Greatest Common Divisor (GCD) and Least Common Multiple (LCM) Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Number Theory -> Division
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 3-4 Question 6
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 5-6 Question 4

• SLV LVS BLS

  In the following expression, different letters represent different digits, and identical letters represent identical digits:

  SLV = LVS + BLS

  Find the number SLV.

  Topics:

  Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rule by 11 Algebra -> Equations Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 5-6 Question 3

• Compose a Sum

  Compose three numbers from the digits `1,2,3,4,5,6,7,8,9` such that one of them is the sum of the other two.
  Each digit must be used exactly once.

  Topics:

  Arithmetic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 3-4 Question 4
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 5-6 Question 1

• How Many Sums Are Possible?

  What is the number of possible results of addition exercises of the form `A + B`
  where A and B are two distinct positive single-digit numbers?

  Topics:

  Arithmetic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 3-4 Question 5

• We went on a trip

  Grade 4, consisting of 32 students, went on a trip. The students had to bring hats, sunglasses, and water bottles.
  No child forgot all of these things, but:

  • Among the students who brought hats, 9 forgot sunglasses,
  • Among the students who brought sunglasses, 7 forgot water bottles,
  • And among the students who brought water bottles, 10 forgot sunglasses.

  How many students in the class brought everything needed for the trip?

  Topics:

  Arithmetic Algebra -> Word Problems Logic -> Reasoning / Logic Set Theory Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 5-6 Question 2

• Five-Digit Palindromic Numbers

  A number is called palindromic if its digits can be read in reverse order, and the result will not change. For example, the number 4407667044 is a palindromic number, and so is 92329.
  How many five-digit palindromic numbers are there in total?

  Topics:

  Arithmetic Combinatorics
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 2

• Question

  In the following addition problem, different shapes replace different digits, and identical shapes replace identical digits:

  `triangle square triangle square triangle+ square triangle square triangle square = o+ triangle triangle triangle triangle o+`

  What is the result of the addition?

  Topics:

  Arithmetic Algebra -> Equations Logic -> Reasoning / Logic Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 3

• The Elevator

  Avi works in a multi-story building, on the top floor. His friends Benny and Gil also work in the same building. Every day, in the morning and evening, Avi goes to greet them.
  In the morning Avi enters the building,

  • goes up 21 floors in the elevator to Benny's office,
  • walks down to Gil's office,
  • goes up 17 floors in the elevator to his office.

  After work,

  • Avi goes down 9 floors in the elevator to Benny's office,
  • walks down to Gil's office,
  • goes down 13 floors in the elevator and exits the building.

  How many floors are in the building? (Reminder - the ground floor is also a floor)

  Topics:

  Arithmetic Algebra -> Word Problems
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 4

• The Truth-Teller and Liar Survey

  13 truth-tellers and 12 liars participated in a survey. In the survey, each participant was asked about every other participant (including themselves) whether they were a truth-teller. How many "yes" answers were received in the survey in total?

  Topics:

  Arithmetic Algebra -> Word Problems Logic -> Reasoning / Logic Logic -> Truth-tellers and Liars Problems
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 5-6 Question 2

• Clock Angle

  How many minutes after 7:00 will the angle between the hour and minute hands be exactly one degree for the first time?
  Note: The clock hands move continuously at a constant speed.

  Topics:

  Arithmetic Algebra -> Word Problems -> Motion Problems Geometry -> Plane Geometry -> Angle Calculation
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 7-8 Question 3
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grade 9 Question 3