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Quiz about Chessbogglers
Quiz about Chessbogglers

Chessbogglers Trivia Quiz


Does the notion of me twisting your brain with chess-related logic problems tickle your fancy? If your reply is in the affirmative do take this quiz before going to the doctor.

A multiple-choice quiz by gentlegiant17. Estimated time: 5 mins.
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Time
5 mins
Type
Multiple Choice
Quiz #
314,214
Updated
Dec 03 21
# Qns
10
Difficulty
Tough
Avg Score
6 / 10
Plays
1523
Awards
Editor's Choice
Question 1 of 10
1. How many legal opening moves does White have if all 16 pawns are removed from the chessboard before start of play? Hint


Question 2 of 10
2. Using its legal moves on an empty chessboard, which of the following pieces is able to complete a route which starts at the bottom-left square (A1), passes through each of the squares exactly once and ends at the top-right square (H8)? Hint


Question 3 of 10
3. What is the minimal number of queens that can be placed on the chessboard such that each and every square is attacked by at least one of them? Hint


Question 4 of 10
4. In a chess tournament with 7 participants, each player is scheduled to play every other player twice. A game winner receives 1/42 points while a loser receives nothing. In a draw, both players receive 1/84 points. How many points will be granted in total once the tournament is over? Hint


Question 5 of 10
5. In how many ways can you place two opposite-coloured rooks on an empty chessboard so that they do not pose an attack on one another? Hint


Question 6 of 10
6. Imagine a chessboard with the top-left (A8) and bottom-right (H1) white squares removed. Can the remaining 62 squares be completely tiled by 31 domino pieces?


Question 7 of 10
7. Two black bishops are placed on the black squares of an empty chessboard. How many positions exist where their paths do not collide? Hint


Question 8 of 10
8. Known as "The Knights Problem", what is the maximum number of knights (regardless of colour) which can be placed on the chessboard so that none of them attacks one another? Hint


Question 9 of 10
9. A chess tournament with 2^k participants is played in an elimination series mode. Is it possible for such a tournament that upon its completion the total number of games played is evenly divisible by 3?


Question 10 of 10
10. Four queens are placed in the four centre squares of an empty chessboard (D4, D5, E4 and E5). Does a fifth piece exist which using its legal moves can move freely between the unattacked squares left on the board? Hint



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Most Recent Scores
Mar 23 2024 : bradez: 7/10
Mar 05 2024 : pwefc: 10/10

Score Distribution

quiz
Quiz Answer Key and Fun Facts
1. How many legal opening moves does White have if all 16 pawns are removed from the chessboard before start of play?

Answer: 50

Each rook has 7 legal moves (including one attack). Each knight has 3. Each bishop has 7. The king has 2 (as it cannot move to D2). The queen has 14 (including one attack). Totaling it up: 2×(7+3+7)+2+14=50. With the pawns in place, the number is 20.
2. Using its legal moves on an empty chessboard, which of the following pieces is able to complete a route which starts at the bottom-left square (A1), passes through each of the squares exactly once and ends at the top-right square (H8)?

Answer: King

The knight cannot perform the task. As it switches square colour on each of its moves, on even-numbered moves it lands on a black square. Thus, after the 62nd move, assuming that it has made it through all the squares besides H8, it is placed on a black square. This means that it cannot reach H8 on its 63rd and last move, since H8 is a black square as well.

The bishop cannot perform the task since it is limited to single-coloured squares.

There are numerous routes for the king to achieve the task. For example, covering the top six rows by N-like and inverted-N-like moves, next dashing from H7 to A7 and from A8 to H8.
3. What is the minimal number of queens that can be placed on the chessboard such that each and every square is attacked by at least one of them?

Answer: 5

This is a variation of the classic "Queens Problem", which belongs to a branch called domination problems. There are 4860 solutions with 5 queens where the queens are allowed to attack each other. When the constraint is added that the 5 queens must be placed on a non-attacking formation, the number of solutions drops to 91. Here is one of them: A1, C7, D3, G8 and H4.
4. In a chess tournament with 7 participants, each player is scheduled to play every other player twice. A game winner receives 1/42 points while a loser receives nothing. In a draw, both players receive 1/84 points. How many points will be granted in total once the tournament is over?

Answer: 1

Regardless of the result, 1/42 points are granted in each of the tournament's games.

The total number of games in the tournament is 7!/5!=42.

42 games, 1/42 points granted per game - 1 point in total is granted throughout the tournament.
5. In how many ways can you place two opposite-coloured rooks on an empty chessboard so that they do not pose an attack on one another?

Answer: 3136

No matter where you place a rook on the board, it poses an attack on 14 squares. Not forgetting to include the square the rook is placed on, the correct calculation is: 64×(64-14-1)=64×49=3136.
6. Imagine a chessboard with the top-left (A8) and bottom-right (H1) white squares removed. Can the remaining 62 squares be completely tiled by 31 domino pieces?

Answer: No

Each domino tile covers one black square and one white square. The chessboard in question has 32 black squares and 30 white squares, which means that the answer to my question is negative.

On the other hand, a generalized theorem exists (Gomory's Theorem) proving that any standard chessboard with one black square and one white square removed can be fully tiled by 31 domino pieces.
7. Two black bishops are placed on the black squares of an empty chessboard. How many positions exist where their paths do not collide?

Answer: 712

A bishop placed on the any of the 14 black squares on an outer boundary of the chessboard poses an attack on 7 other black squares. As you move into the centre of the board the number increases to 9, 11 and finally 13 on the two centre black squares (D4 and E5). A summation on all options gives 14×(32-7-1)+10×(32-9-1)+6×(32-11-1)+2×(32-13-1)=712.
8. Known as "The Knights Problem", what is the maximum number of knights (regardless of colour) which can be placed on the chessboard so that none of them attacks one another?

Answer: 32

A knight can pose an attack only on a square with a different colour than the one it stands on. Hence, when 32 knights are placed on 32 same-colour squares none of them attacks one another. Without formally proving it here, it is pretty intuitive to see that any formation which involves placing knights on different coloured squares results in a lower number.
9. A chess tournament with 2^k participants is played in an elimination series mode. Is it possible for such a tournament that upon its completion the total number of games played is evenly divisible by 3?

Answer: Yes

The first elimination round has 2^(k-1) games, the second one 2^(k-2) and so forth till we reach the final.
The total number of games is always (2^k)-1 which is the sum of the geometric series 1,2,...,2^(k-2),2^(k-1).
There are infinitely many instances where (2^k)-1 takes a value evenly divisible by 3 (e.g. 3 for k=2 and 63 for k=6).
10. Four queens are placed in the four centre squares of an empty chessboard (D4, D5, E4 and E5). Does a fifth piece exist which using its legal moves can move freely between the unattacked squares left on the board?

Answer: Yes, a queen

Symmetry considerations give away the queen while ruling out the other three options. Only a queen can roam freely between the unattacked squares of this formation (A3, A6, C1, C8, F1, F8, H3 and H6).
Source: Author gentlegiant17

This quiz was reviewed by FunTrivia editor ozzz2002 before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system.
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