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Found: 5

Problem #PRU-103869

Problems Set theory and logic Order relations Methods Pigeonhole principle Pigeonhole principle (other)

11–13 2.0

Solve the puzzle: \(BAO \times BA \times B = 2002\).

Problem #PRU-31368

Problems Set theory and logic Order relations

10–13 2.0

The numbers from 1 to 9999 are written out in a row. How can I remove 100 digits from this row so that the remaining number is a) maximal b) minimal?

Problem #PRU-32132

Problems Methods Extremal principle Extremal principle (other) Set theory and logic Order relations Algebraic methods Proof by exhaustion

13–15 3.0

The order of books on a shelf is called wrong if no three adjacent books are arranged in order of height (either increasing or decreasing). How many wrong orders is it possible to construct from \(n\) books of different heights, if: a) \(n = 4\); b) \(n = 5\)?

Problem #PRU-88325

Problems Set theory and logic Mathematical logic Mathematical logic (other) Order relations

11–13 2.0

In the race of six athletes, Andrew lagged behind Brian and two more athletes. Victor finished after Dennis, but before George. Dennis beat Brian, but still came after Eustace. What place did each athlete take?

Problem #PRU-98016

Problems Combinatorics Integer lattices Integer lattices (other) Set theory and logic Order relations Methods Pigeonhole principle Pigeonhole principle (other)

10–15 4.0

We are given 101 rectangles with integer-length sides that do not exceed 100.

Prove that amongst them there will be three rectangles \(A, B, C\), which will fit completely inside one another so that \(A \subset B \subset C\).