Deduction - Puzzle Prime

Buried Up to Neck

Section: Brain Teasers Category: Deduction

Difficulty: Medium

Three friends, Adam, Bob, and Charlie are buried in the sand up to their necks, all facing West. Charlie can see both Adam and Bom, Bom can see only Adam, and Adam cannot see anyone. Black and white hats are placed on their heads. The three friends are told that there is at least one hat from each color, and then they are asked whether anyone can guess the color of their own hat.

After a few minutes, one of them answers. Who is that?

SOLUTION

If Adam and Bob had hats with identical colors, then Charlie would immediately be able to deduce that his hat has the opposite color. Charlie doesn’t do that, so Adam and Bob are able to figure out that their hats have opposite colors. Since Bob is the one who can see the color of Adam’s hat, he is the one that answers the question.

Unknown Author February 13, 2024

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Third Business Day

Section: Brain Teasers Category: Deduction

Difficulty: Medium

What is the chance that the third business day of a month is Wednesday?

SOLUTION

Assuming there is an equal chance that the given month begins with any of the seven days of the week, the answer is 3/7. That’s because Saturday and Sunday are non-working days, and therefore if the month starts with any of them, the third business day will still be Wednesday.

We note that 3/7 is actually an approximation of the actual answer, since the frequencies with which the days of the week appear as first in a given month, are close to but not equal to 1/7 each.

Unknown Author December 28, 2023

2 Comments

Mirrors

Section: Brain Teasers Category: Deduction

Difficulty: Advanced

Why do mirrors flip left and right but do not flip up and down?

SOLUTION

Solution coming soon.

Unknown Author December 7, 2023

3 Comments

Sunome Variations

Section: Brain Teasers Category: Deduction

Difficulty: Advanced

The main challenge of a Sunome puzzle is drawing a maze. Numbers surrounding the outside of the maze border give an indication of how the maze is to be constructed. To solve the puzzle you must draw all the walls where they belong and then draw a path from the Start square to the End square.

The walls of the maze are to be drawn on the dotted lines inside the border. A single wall exists either between 2 nodes or a node and the border. The numbers on the top and left of the border tell you how many walls exist on the corresponding lines inside the grid. The numbers on the right and bottom of the border tell you how many walls exist in the corresponding rows and columns. In addition, the following must be true:

Each puzzle has a unique solution.
There is only 1 maze path to the End square.
Every Node must have a wall touching it.
Walls must trace back to a border.
If the Start and End squares are adjacent to each other, a wall must separate them.
Start squares may be open on all sides, while End squares must be closed on 3 sides.
You cannot completely close off any region of the grid.

In addition, these variations of Sunome have the following extra features:

Paths (borders with a hole in the middle) designate places where the solution should pass through.
Pits (black squares) designate places where the solution does not pass through.
Portals (circled letters) designate places where the solution should pass through and teleport from one portal to the other.
Sunome Cubed is solved similarly but on the surface of a cube. The numbers on the top right, top left, and center left of the border tell you how many walls exist on the corresponding pairs of lines inside the grid. The numbers on the center right, bottom right, and bottom left of the border tell you how many walls exist in the corresponding pairs of rows/columns.

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

SOLUTION

The solutions are shown below.

Adam Bontrager December 4, 2023

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The Four Oaks

Section: Brain Teasers Category: Deduction

Difficulty: Advanced

A father left to his four sons this square field, with the instruction that they divide it into four pieces, each of the same shape and size, so that each piece of land contained one of the trees. How did they manage it?

SOLUTION

The solution is shown below.

Sam Loyd November 10, 2023

2 Comments

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Imprisoned Logicians

Section: Brain Teasers Category: Deduction

Difficulty: Expert Tags: Featured

Two friends, logicians – Ein and Stein – get imprisoned in two distant cells in a castle. Both cells have just one door, and a window with 8 bars in the first cell, and 12 bars in the second cell. The first day both logicians get the same letter from the prison master:

“The total number of bars in the two prison cells in this castle is either 18 or 20. Starting tomorrow, every morning I will go first to Ein and then to Stein, and will ask how many bars the other logician has. If one of you answers correctly, I will immediately let both of you leave the castle. If one of you answers incorrectly, I will execute both of you. Of course, you can always decide not to answer and just stay imprisoned.
I have sent a copy of this letter to you and your friend. There is no point in trying to communicate with him – your cells are far away from each other, and he won’t hear you.”

Will the logicians manage to escape the castle eventually? When will they do it?

SOLUTION

Solution coming soon.

Unknown Author October 1, 2023

7 Comments

Get One Hundred

Section: Brain Teasers Category: Deduction

Difficulty: Advanced

9 8 7 6 5 4 3 2 1 = 1 0 0

Add +, +, +, – anywhere above in order to get a valid equality.

SOLUTION

The answer is:

9 8-7 6+5 4+3+2 1 = 1 0 0

Unknown Author September 28, 2023

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Five Points, Ten Distances

Section: Brain Teasers Category: Deduction

Difficulty: Medium

Five points, A, B, C, D, and E, lie on a line. The distances between them in ascending order are: 2, 5, 6, 8, 9, X, 15, 17, 20, and 22. What is X?

SOLUTION

We assume that the points are ordered A to E from left to right. We have AE = 22 and either AD = 20, BE = 17, or AD = 17, BE = 20. Without loss of generality AD = 20, BE = 17, and therefore AB = 5, BD = 15, DE = 2. The distance of 6 is associated with either BC or CD, and therefore the points are arranged in one of these two ways: