“T” Days
There are four days which start with the letter “T” – Tuesday, Thursday, and which two others?
SOLUTION
“Today” and “tomorrow”.
Fair Split
It is well known how to split fairly a cake between two people – one of them cuts, the other one picks. The question is, how can you split fairly a cake between three people?
Easy: “Fairly” means that every person gets at least 1/3 of the cake.
Hard: “Fairly” means that every person has the opportunity to get at least as much
SOLUTION
Easy (Banach-Knaster method):
The first person cuts 1/3 piece of the cake. If the second person thinks it is larger than 1/3, he can trim it to 1/3. If the third person thinks the cut (and possibly trimmed) piece is larger than 1/3, he can trim it to 1/3 and keep it. Otherwise, the second person takes the piece if he decided to trim it, or the first one, in case he did not. After that, there are two people left, and they can easily split the remaining cake between them. This approach works for any number of people.
Hard (Selfridge-Conway method):
The first person cuts the cake in 3 pieces. The second one takes the biggest piece and trims it so that it becomes as large as the second biggest piece, puts the trimmings aside. The third person picks one of the three big pieces. Then, if the trimmed piece is still available, the second person takes it, if not – he picks whichever he likes. The first person takes the last remaining big piece. Among the first two people, whoever did not pick the trimmed big piece, splits the trimmings
Two Solid Cubes of Lead
You have two solid cubes of lead, which have almost the same size. You cut a hole in one of them and pass the other one through it. After measuring the cubes later, it turns out that the larger cube is still heavier than the smaller one. How is this possible?
SOLUTION
You cut a hole in the SMALLER cube, and pass the larger cube through it. “Prince Rupert’s cube” is the largest cube which can pass through a unit cube, and it is approximately 6% larger.
Shapes Reunion
Can you help square find his way back to his friends? On the way, look out for:
- one red crescent;
- two yellow circles, connected by a yellow line;
- three blue crosses in a row;
- a block with four pairs of leaves and five blue lines on an orange block.
SOLUTION
The solution is shown below.
Tie a Knot
First, get a completely untangled rope. Now, your task is to grab its two ends, and without letting it go, tie this knot in the middle.
SOLUTION
In order to do this, first cross your arms, and from this position, grab the two ends of the rope. Once you untangle your arms, the knot will appear on the rope.
Detective Flanders and the Zodiac Killer (Guide)
“Detective Flanders and the Zodiac Killer“ is a puzzle story, exclusively created for Puzzle Prime. Every chapter you read contains a puzzle that must be solved in order to continue further.
Here you can find a walkthrough guide to the story, created by andante. Thank you for the wonderful work!
If you need more help, feel free to ask questions and the discuss the puzzles in the comments section. However, please do not share the answers and only stick to hints instead.
Inertia
Can you see which letters are connected with each other in this 3D maze?
SOLUTION
The solution is shown below.
When You Have Me
When you have me, you want to share me.
When you share me, you no longer have me.
SOLUTION
The answer is SECRET.
Curve in a Box
Is it possible to design a simple closed curve inside a box, such that its projections on all 6 walls of the box are trees, i.e. curves without loops?
SOLUTION
Yes, it is possible, as shown on the image below.
