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• Question

  There are three sacks of nuts. The first sack has `6` kilograms of nuts less than the other two sacks combined. The second sack has `10` kilograms of nuts less than the other two sacks combined.

  How many kilograms of nuts are in the third sack?

  Topics:

  Algebra -> Equations Algebra -> Word Problems

• Question - Shlomi's Schedule

  Shlomi dedicates `1/3` of his time to playing games on the tablet, `1/5` of his time to studying at school, `1/6` to watching movies, `1/70` to solving mathematical problems, and `1/3` to sleeping.

  Is it possible to live like that?

  Topics:

  Algebra -> Inequalities Arithmetic -> Fractions

• Question - Clock Tower

  A bell in a clock tower rings `3` times in `12` seconds. How long does it take to ring `6` times?

  Topics:

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

• Question - Mitzi

  There are many cats named Mitzi. Which is more numerous: cats excluding the cats that are not named Mitzi, or animals named Mitzi excluding those that are not cats?

  Topics:

  Logic -> Reasoning / Logic Set Theory

• Question - Corruption in Parliament

  The parliament of the magical country consists of `20` people. It is known that among the `20` members of parliament, there is at least one who is not corrupt. Additionally, it is known that for any two members of parliament we choose, one is necessarily corrupt. How many members of parliament of the magical country are corrupt?

  Topics:

  Algebra -> Inequalities Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures

• Question - Three Friends

  There are three friends, Weiss, Schwartzman, and Rotenberg. This trio of friends is special because one of them is blonde, one is ginger (redhead), and one has black hair. One day, the blonde guy said to Schwartzman: "We are a very special trio of friends! Notice that it's not only that the last names of the three of us mean colors, but also that each of our last names does not match his hair color."

  What hair color does each of these three people have?

  Note: "Schwartzman" means "black man", "Rotenberg" means "red mountain" and "Weiss" means "white" (from Yiddish).

  Topics:

  Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Combinatorics -> Number Tables Logic -> Truth-tellers and Liars Problems

• Question

  One-seventh of mathematicians are philosophers, and one-ninth of philosophers are mathematicians. Which are there more of – philosophers or mathematicians?

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  Topics:

  Algebra -> Word Problems Logic -> Reasoning / Logic Arithmetic -> Fractions

• Question

  In a school, there are `400` students. Prove that there exist two students who celebrate their birthday on the same date of the year.

  Topics:

  Combinatorics -> Pigeonhole Principle

• Question

  In a company, there are `30` employees. The youngest is `20` years old, and the oldest is `45` years old. Is it necessarily true that there are people in this company who are the same age?

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  Topics:

  Combinatorics -> Pigeonhole Principle

• Question - Continue the Sequence

  `2, 6, 12, 20, 30…`

  a. What is the next number (the sixth) in the sequence?

  b. What is the `2016`th number in the sequence?

  Topics:

  Arithmetic Logic -> Reasoning / Logic Algebra -> Sequences -> Arithmetic Progression / Arithmetic Sequence Algebra -> Sequences -> Complete/Continue the Sequence