Calendar Puzzle

2026-02-23. Filed in public, twoville.

I have created the world's most boring puzzle. Each piece is a month of the year. Together they form the calendar. Here's 2026, which started on a Thursday:

Note that February is a rectangle in 2026. February is the only month that can be a rectangle, but this only happens when the year starts on a Thursday. It will more often be an octagon. Other months are either a hexagon or an octagon. The only time that February will be a hexagon is in a leap year that starts on Thursday.

If you don't believe me, experiment by changing the starting weekday in this Twoville program to values in [0, 6]:

let months = {
  31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31
}

let weekday = 4
let y = 0.0

for month in months
  // How many days are in the partial top and bottom rows?
  let daysInTop = (7 - weekday) % 7
  let daysInBottom = (month - daysInTop) % 7
  
  // How many week rows do we need? +6 gives us the ceiling
  // of the quotient.
  let rowCount = (month + weekday + 6) / 7
    
  polygon
    color = [0.8, 0.4, 0.6]
    stroke.weight = 0.2

// Start drawing at the top-right corner since all months
    // will have a clear top-right corner. From there, we wind
    // around counter-clockwise.
    vertex.position = [7, y]
    
    // Top
    if weekday == 0
      vertex.rposition = [-7, 0]
    else
      vertex.rposition = [-daysInTop, 0]
      vertex.rposition = [0, -1]
      vertex.rposition = [-weekday, 0]

// Left
    vertex.rposition = [0, -(month - daysInTop + 6) / 7]
    
    // Bottom
    if daysInBottom == 0
      vertex.rposition = [7, 0]
    else
      vertex.rposition = [daysInBottom, 0]
      vertex.rposition = [0, 1]
      vertex.rposition = [7 - daysInBottom, 0]

weekday = (weekday + month) % 7
  y = y - rowCount - 0.5

view
  autofit = true
  margin = 0.2

let months = {
  31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31
}

let weekday = 4
let y = 0.0

weekday = (weekday + month) % 7
  y = y - rowCount - 0.5

view
  autofit = true
  margin = 0.2

I won't be lasercutting this puzzle.