6 Axis Logic Grid Puzzle

Here is the first logic grid puzzle I’ve designed in about 15 years, written for the XKCD forums.  I normally don’t post language-based puzzles but the forum only allows text posts for new users.  The community at logic-puzzles.org has worked this one out.  Well Done BlackFiresong.  See the full article for spreadsheets and solutions.

Introduction

Here is a 6-axis logic grid puzzle with an F1 Racing theme.  Everything I know about F1 racing I googled today, so actual knowledge is neither necessary nor helpful.  Names of manufacturers, car numbers, drivers, and countries of origin have all been fictionalized.  A driver with a German sounding name is not necessarily from Germany, and a team can be from any country, regardless of its real-world origin.  The only correlations come from the following clues.

Structure

There are 6 drivers with the following names:
  • Daniel
  • Max
  • Sebastian
  • Nico
  • Kimi
  • Romain
Each driver is from one of the following 6 countries, one driver per country:
  • Germany
  • UK
  • Norway
  • Sweden
  • Japan
  • USA
Each driver is on one of the following teams, one driver per team:
  • Red Bull
  • Ferrari
  • Mercedes
  • Haas
  • McLaren
  • Renault
Each driver has a car with a unique number from one to six, one number per driver.
Each driver placed in first through sixth place in the qualifying round and each driver placed first through sixth in the final race.  There were no ties.
There is a total of six axes: Name, Country, Team, Car Number, Qualifying Position, and Final Position.
Identify all values for each driver.

Clues

  1. Every team whose name has an adjacent pair of identical letters is associated with an odd-numbered car.
  2. For every driver whose name has fewer than three vowels:
    1. The difference between the qualifying position and final position is odd.
    2. The sum of the qualifying position, final position, and car number is a prime number.
  3. For the driver from Germany:
    1. Car number < qualifying position < final position.
    2. The sum of these three numbers is a prime number.
  4. For the Red Bull driver:
    1. Car number > qualifying position > final position.
    2. The sum of these three numbers is a prime number.
  5. For the driver from Norway:
    1. Qualifying position and final position are the same.
    2. The sum of the qualifying position, final position, and car number is a prime number.
  6. For the driver from UK:
    1. The sum of the qualifying position, final position, and car number is 10.
  7. Daniel doesn’t drive for Haas.
  8. Daniel is not from Norway.
  9. If you were to arrange the list of teams and the list of countries in alphabetical order and place them side by side, there would be no correlations. (The alphabetically first team is not from the alphabetically first country, second team is not from the second country, etc.)
  10. If you were to arrange the list of names and the list of countries in alphabetical order and place them side by side, there would be exactly two correlations.
  11. Sebastian’s final position is divisible by 3.
  12. Japan’s qualifying position is divisible by 3.
  13. Sebastian is not from the UK.
  14. Ferrari is not from the UK.
  15. Romain is not in car number 1.
  16. Either Nico or Kimi is from the USA.
  17. The McLaren team placed neither 1st nor 6th in the qualifying round.
  18. Mercedes is not driven by Max.

Logic Grid F1 - Solving Grid

Continue reading “6 Axis Logic Grid Puzzle”

Trapezoids

Here is a new type loosely inspired by Inaba Naoki’s Cell-Land.

Rules

Shade some cells such that:

  1. Numbers indicate exactly how many surrounding cells are filled.
  2. Filled cells must be in clusters of 3, forming trapezoids.  A trapezoid may not share an edge with another trapezoid.
  3. All unfilled cells are connected edge-to-edge.

Example

Hidden Trapezoids ExampleHidden Trapezoids Example Solution

Puzzles

All of the puzzles can be found organized in this printable PDF, or in the images below.

PDF Trapezoids

01. Easy

Hidden Trapezoids Easy 01.png

02. Medium

Hidden Trapezoids Medium 02

03. Medium

Hidden Trapezoids Medium 03

04. Hard

Hidden Trapezoids Hard 04

05. Hard

Hidden Trapezoids Hard 05

06. Hard

Hidden Trapezoids Hard 06

07. Expert

Hidden Trapezoids Expert 07

Truncated Square Chocona

Chocona (チョコナ) is a puzzle type that likely originates with Nikoli.  I have adapted it to play on a Truncated Square grid.

Rules

Shade some cells such that:

  1. A filled square may not share an edge with a filled octagon.
  2. Filled octagons may share an edge, but only if the contiguous area of filled octagons forms a 45° oriented rectangle.
  3. Each bold-outlined region must have at least one filled octagon.
  4. Numbers indicate exactly how many cells, octagon or square, are filled in a bold-outlined region.  Regions with no number can have any number of filled cells.

Example

 Truncated Square Chocona ExampleTruncated Square Chocona Example Solution

Puzzles

All of the puzzles can be found organized in this printable PDF, or in the images below.

PDF Truncated Square Chocona

01. Easy

Truncated Square Chocona Easy 01

02. Medium

Truncated Square Chocona Medium 02

03. Medium

Truncated Square Chocona Medium 03

04. Hard

Truncated Square Chocona Hard 04

05. Hard

Truncated Square Chocona Hard 05

06. Hard

Truncated Square Chocona Hard 06

07. Expert

Truncated Square Chocona Expert 07