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Cheryl’s Birthday

Section: Brain Teasers Category: Deduction

Difficulty: Advanced Tags: Featured

Cheryl’s birthday is one of 10 possible dates:

May 15
May 16
May 19
June 17
June 18

July 14
July 16
August 14
August 15
August 17

Cheryl tells the month to Albert and the day to Bernard.

Albert: I don’t know the birthday, but I know Bernard doesn’t know either.
Bernard: I didn’t know at first, but now I do know.
Albert: Now I also know Cheryl’s birthday.

When is Cheryl’s birthday?

SOLUTION

If Albert knows that Bernard doesn’t know when the birthday is, then the birthday can’t be on May 19 or June 18. Also, Albert must know that the birthday can’t be on these dates, so May and June are completely ruled out.

If Bernard can deduce when the birthday is after Albert’s comment, then the birthday can’t be on 14th. The remaining possibilities are July 16, August 15, and August 17.

Finally, if Albert figures out when the birthday is after Bernard’s comment, then the date must be July 16.

Unknown Author June 13, 2020

19 Comments

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Puzzle Tournament 2

Section: Contests Category: Tournament

Tags: Featured

Puzzle Prime’s second puzzle tournament was organized on June 27, 2020. Congrats to Elyot G. who solved all the puzzles! You can see the problems and the rankings below.

You have 60 minutes to solve 6 puzzles, each worth 1 point. Upload your solutions as a pdf, document, or image, using the form below. Good luck!

Time for work: 1 hour

Puzzle Prime Knight

Start from a square with a P on the chessboard, and keep jumping via knight’s move, consequently landing on squares with the letters U-Z-Z-L-E-P-R-I-M-E.

Point of View

8 of these diagrams correspond to views of the object in the corner when it is looked from different perspectives. Which 2 aren’t?

Note: The projections below are parallel (not perspective).

Chess Fight

Choose a chess piece on the board. Then, move the piece to a cell with another piece, and remove the first piece. Repeat, by moving the second piece to a cell with a new piece, and removing it. Continue until there is only one piece remaining on the board.

Note: For example, we can move the Queen on d2 to the Bishop on b2, the Knight on c3, or the Bishop on d4. If we move the Queen to d4 and remove it from the board, then we must move the Bishop on d4. The only available cell is c3, where a Knight is positioned. We must remove the bishop and move the Knight on c3 either to the Rook on b1 or the Rook on a2…

Special Date

On April 5, 2013 (5.4.2013), the digits used for expressing the date were all different and consecutive. When was the last date before it with this property?

Remark: The digits 9 and 0 are not consecutive.

Splitting the Area

You have 1 square with side length 1 and 2 circles with diameter length 1. Draw a single line so that the resulting areas on the left and on the right of the line are equal.

Notes: You need to specify how you find a line satisfying the condition above.

Chess Connect

The starting and ending positions of 6 chess pieces are shown on the board. Find the trajectories of the pieces, if you know that they do not overlap and completely cover the board.

Notes: The pieces can not backtrack. Two trajectories can intersect diagonally but can not pass through the same square. Only the Knight has a discontinuous trajectory.

Solutions

The answer to Point of View is C and J.
The answer to Special Date is 23.4.1765.
The solutions of the other puzzles are shown below.

Results

Puzzler	P1	P2	P3	P4	P5	P6	Total
Elyot G.	1	1	1	1	1	1	6
David R.	1	0	1	0	1	1	4
Rodrigo R.	1	0.5	1	0	0	1	3.5
N	1	0	1	0	1	0	3
Hristo H.	0	0	1	0	1	0	2
Rockmosis	1	0	1	0	0	0	2

Prizes

#1.
$10 Gift Card (iTunes or Play Store)
Puzzle Avatar (custom made)
Puzzle Pelago (mobile game by Hallgrim Games)
Hook (mobile game by Rainbow Train)

#2.
$5 Gift Card (iTunes or Play Store)
Puzzle Avatar (custom made)
Puzzle Pelago (mobile game by Hallgrim Games)
Hook (mobile game by Rainbow Train)

#3.
Puzzle Avatar (custom made)
Puzzle Pelago (mobile game by Hallgrim Games)
Hook (mobile game by Rainbow Train)

#4-5.
Puzzle Pelago (mobile game by Hallgrim Games)
Hook (mobile game by Rainbow Train)

Puzzle Prime June 1, 2020

1 Comment

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Cut and Arrange

Section: Brain Teasers Category: Practical

Difficulty: Advanced Tags: Featured

Get a piece of paper with dimensions 9×12 with a 1×8 rectangular hole in the middle. Then, cut the paper into two pieces that can be arranged into a square. You can print out the shape below.

SOLUTION

The solution is shown below.

Unknown Author May 13, 2020

0 Comments

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Schoolyard

Section: Brain Teasers Category: Insight

Difficulty: Easy Tags: Featured

Draw 2 squares in the schoolyard in order to separate all students from each other.

SOLUTION

The solution is shown below.

Unknown Author May 10, 2020

1 Comment

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10 Dots, 10 Coins

Section: Brain Teasers Category: Mathematics

Difficulty: Expert Tags: Featured

If you have 10 dots on the ground, can you always cover them with 10 pennies without the coins overlapping?

SOLUTION

Assume the dots lie in a plane and the radius of a penny is 1. Make an infinite grid of circles with radii 1, as shown on the picture, and place it randomly in the plane.

If we choose any point in the plane, the probability that it will end up inside some circle of the grid is equal to S(C)/S(H), where S(C) is the area of a coin and S(H) is the area of a regular hexagon circumscribed around it. A simple calculation shows that this ratio is larger than 90%. Therefore, the probability that some chosen point in the plane will not end up inside any circle is less than 10%. If we have 10 points, the probability that neither of them will end up inside a circle is less than 100%. Therefore, we can place the grid in the plane in such a way that every dot ends up in some circle. Now, just place the given coins where these circles are.

Source:

The Mathematical Intelligencer, 34:3 [September 2012], 11-14

Naoki Inaba April 10, 2020

2 Comments