Logic, Reasoning / Logic

This category emphasizes general logical reasoning skills, often applied to puzzles or scenarios not strictly formal. It involves deduction, inference, identifying patterns, and drawing sound conclusions from given information. It overlaps with formal logic but can be broader.

• 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

• Question

  A two-digit number is written on the board.
  Avi said: "The units digit of the number is 3"
  Beni said: "It's a square number"
  Gili said: "This number is a multiple of 12"
  Then the teacher said: "There are two correct statements and one wrong one here."
  What number was written on the board?

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  Topics:

  Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules Logic -> Reasoning / Logic Logic -> Truth-tellers and Liars Problems
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage B, Grades 3-4 Question 1

• 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

• Question

  A two-digit number is written on the board.
  Avi said: "The digit 5 appears in this number."
  Beni said: "This is a square number."
  Gili said: "This number is greater than 50."
  Dani said: "The number is divisible by 7."
  Then the teacher said: "There are three correct statements here and one incorrect statement.".
  What number was written on the board?

  Topics:

  Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage B, Grades 5-6 Question 1

• 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

• How Many Liars?

  A tourist is traveling in a land of liars and truth-tellers. All truth-tellers always tell the truth, and all liars always lie.
  The tourist meets four friends: Alice, Betty, John, and Donald, and asks them: "How many of the four of you are liars?"
  Alice answers: 0
  Betty answers: 1
  John answers: 2
  Donald answers: 3
  Can we know for certain how many of them are liars?

   

  Topics:

  Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Logic -> Truth-tellers and Liars Problems
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Final, Grades 3-4 Question 1

• Donkey in the Middle

  Avi, Beni, and Gadi played "Donkey in the Middle" - at any moment someone stands in the middle and tries to catch a ball that the other two are passing. If he succeeds, one of the other two replaces him.
  After the game, it turned out that Avi stood in the middle 8 times, Beni 4 times, and Gadi 13 times.
  Who was the first and who was the last to stand in the middle?

  Topics:

  Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Final, Grades 3-4 Question 3

• Doughnuts

  Ayala, Benny, Gili, Danny, and Hadas received a package of doughnuts containing

  • 10 doughnuts with dulce de leche
  • 8 doughnuts with peanut butter
  • 9 doughnuts with chocolate
  • 11 with strawberry jam

  Each of them has their favorite type of doughnut.

  • Ayala ate 5 doughnuts of her favorite type
  • Benny ate 6 doughnuts of his favorite type
  • Gili ate 7 doughnuts of her favorite type
  • Danny ate 8 doughnuts of his favorite type
  • Hadas ate 9 doughnuts of her favorite type

  After that, they were left with 3 doughnuts of different types. What is each of their favorite type of doughnut?

  Topics:

  Arithmetic Algebra -> Word Problems Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Final, Grades 3-4 Question 5

• 6 on the Board

  The number 6 is written on the board. At each step, you can add the digit 6 to the end of the number (so that it is the units digit,) or replace the number with the sum of its digits.
  Which numbers can be obtained in this way? Describe the entire set of numbers and explain why there are no more

  Topics:

  Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rules by 3 and 9 Combinatorics -> Induction (Mathematical Induction) Logic -> Reasoning / Logic Number Theory -> Division -> Parity (Even/Odd) Algebra -> Sequences Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Final, Grades 3-4 Question 6
  • Young Mathematician Olympiad, 2018-2019, Final, Grades 5-6 Question 5

• Another Donkey in the Middle

  Avi, Beni, and Gadi played "Donkey in the Middle" - at any given moment, someone is in the middle, trying to catch a ball that the other two are passing to each other.
  If he succeeds, one of the other two replaces him. After the game, Avi said that he was in the middle 8 times,
  Beni said he was in the middle 4 times, and Gadi forgot how many times he was in the middle.
  They also remember that Beni was the last one in the middle. Describe all the possibilities for the number of times Gadi was in the middle,

  Topics:

  Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Final, Grades 5-6 Question 3