Toasting Bread

Your toaster is broken, so you decide to toast your bread in a pan. The pan can hold three slices of bread at a time and takes 1 minute to toast one of their sides. How much time would it take you to toast four slices of bread on both sides using the pan?

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Puzzle Tournament 4

Puzzle Prime’s fourth puzzle tournament was organized on February 26, 2022. Congrats to REDCROUTONS who solved all the puzzles (even found a small mistake in one of them)!

REDCROUTONS

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

Each problem is worth 1 point. Use the form at the bottom of the post to send your solutions.

1. The Grid

by Puzzle Prime

Figure out how the last portion (7×5 in yellow) of the grid should be colored in black and white.

2. Hexado

by Dr. DJ Upton

Place arrows along hexagon edges so that the number of arrows pointing to each hexagon equals the number of dots inside, adhering to the following rules:

  1. Arrows cannot be touching.
  2. Arrows cannot be placed on dashed edges.

3. Segments

by Puzzle Prime

Use at most 27 segments to create the largest number with distinct digits.

Notes: For example, the number 273914 would use 5+3+5+6+2+4=25 segments.

4. Constellations

by Raindrinker

Connect the stars with lines, so that the number inside each star corresponds to the number of lines connected to it, and the number outside each star corresponds to the total number of stars in its group.

Note: No line connecting two stars can pass through a third star.

5. Chess Connect

by Puzzle Prime

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.

6. Broken Square

by Puzzle Prime

Use exactly 5 out of these 16 pieces to build a 7×7 grid, without overlapping.

Note: You can rotate the pieces, but you cannot mirror them.

100 Guests in 99 Rooms

One hundred people entered a hotel that had 99 rooms, and each of them asked for their own room. In order to solve the problem, the bellboy did the following:

He asked the 100th guest to wait for a while with the 1st guest in room number 1, so that there were 2 guests inside. Then he took the 3rd guest to room number 2, the 4th guest to room number 3, and so on, until finally taking the 99th guest to room number 98. At the end he returned to room number 1 and took the 100th guest to room number 99, which was still vacant.

How could everybody get their own room?

Died on the Fourth of July

During a trivia night, the following question appeared:

“Among the first five US presidents, Washington, Adams, Jefferson, Madison, and Monroe, there were 3 who died on the fourth of July. Can you guess which ones?”

After nobody answered the question, the following hint was given:

“These three presidents were consecutive ones.”

Then, all contestants immediately managed to answer the question. Can you?

27 Figures of Speech

Find 27 figures of speech in the illustration by Ella Baron below.

Limbs

Partition the grid into disjoint “creatures”​, according to the following rules:

  1. Each creature is defined as a shape of 4 connected branches that are each 1 cell wide.
  2. For each creature, one of the branches ends up with a HEAD (always clued) and the other three branches end up with LIMBS (whenever clued, their directions matter).
  3. A creature can never occupy a 2×2 region of cells and can never touch itself.

Examine the first example, then solve the other three puzzles.