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.

• Sum of Products of Digits

  Let `P(n)` denote the product of the digits of the number `n`. For example, `P(1948) = 1 * 9 * 4 * 8 = 288`.

  A.

  Calculate `P(1) + P(2) + P(3) + ... + P(2016)`

  B.

  Find the maximum value of `{P(n)} /n`, where `2016 <= n <= 5777`.

  (Solution format: "x, y/z" where y/z is an unreduced fraction. For example "10000, 35/100")

  Show hint

  Log in here to receive the hint
  Topics:

  Arithmetic Algebra -> Word Problems Combinatorics -> Number Tables Number Theory -> Division
  Sources:
  • Gillis Mathematical Olympiad, 2016-2017 Question 2

• Question

  The numbers with a digit sum of 28 are written on the board in ascending order. What is the 24th number among them?

  Topics:

  Arithmetic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 5-6 Question 2

• Question

  Find the smallest two-digit number `☺` that satisfies:

  `☺times☺ - ☺ = 600`

  Topics:

  Number Theory Arithmetic Algebra -> Equations
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 5-6 Question 5

• Number Network

  In the diagram, the numbers on the edges indicate the differences between the numbers inside the circles. Place positive numbers inside the circles and discover what the number in the bottom circle is.

  

  Topics:

  Arithmetic Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 5-6 Question 6

• Letter Replacement

  Each letter represents a different digit; whenever a specific letter appears, it is necessarily the same digit.

  Find `B-E/2`

  Given: `AB*C=DE`

  And also `F^D=GF`

  Show hint

  Log in here to receive the hint
  Topics:

  Number Theory -> Prime Numbers Arithmetic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Number Theory -> Division Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic

• Question

  Vered subtracted a number composed of the same digits written in reverse order from a three-digit number.
  As a result, she obtained a two-digit number. Find the two-digit number she obtained.

  Topics:

  Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules Algebra Logic -> Reasoning / Logic
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage B, Grades 3-4 Question 2

• Candies

  In a class, there are a number of students and each has a number of candies:
  There are exactly 10 children with at least one candy,
  Exactly 8 children with at least two candies,
  Exactly 6 children with at least 3,
  Exactly 4 children with at least 4,
  And exactly 2 children with 5 candies.
  It is known that no one has more than 5 candies. How many candies are there in the class?

  Topics:

  Arithmetic Algebra -> Word Problems
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage B, Grades 3-4 Question 4
  • Young Mathematician Olympiad, 2018-2019, Stage B, Grades 5-6 Question 3

• 2 or 5 but not 3

  How many two-digit numbers are divisible by 2 or 5, and not divisible by 3?

  Topics:

  Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules Number Theory -> Division
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage B, Grades 3-4 Question 6

• Minimal Table

  Given a table of size `3 times 3`. Hilla wants to write digits from 1 to 9 in the table's cells, such that all the sums in the rows and columns of the table are different, and the total sum of the table is as small as possible.
  It is allowed to repeat the same digit multiple times. What is the smallest sum that Hilla can obtain?

  Topics:

  Arithmetic Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Combinatorics -> Number Tables
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage B, Grades 5-6 Question 7

• Parentheses

  Add parentheses to make the result as large as possible:

  `10000-1000-100-10-1`

  Topics:

  Arithmetic Algebra -> Equations Minimum and Maximum Problems / Optimization Problems
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Final, Grades 3-4 Question 2
  • Young Mathematician Olympiad, 2018-2019, Final, Grades 5-6 Question 1