Futoshiki is a number grid where the clues are mostly greater-than and less-than signs. Fill every row and column with each digit once, and make every sign between neighboring squares true. Every puzzle here has exactly one solution and can be solved by logic alone.
The rules
The grid is 4×4 on Easy, 5×5 on Normal, 6×6 on Hard and 7×7 on Expert, using the digits 1 up to the grid size.
Each row and each column holds every digit exactly once.
A sign between two squares must hold: the point faces the smaller digit and the open side faces the bigger one. Between squares in a column, ∧ means the top digit is smaller and ∨ means the bottom digit is smaller.
A few squares may start filled in. These can’t be changed.
Start with the ends of the range
The smallest and largest digits are the easiest to rule out. A square on the small side of any sign can never hold the largest digit, and a square on the big side can never hold 1. Look for rows and columns where only one square is left that can take the largest digit or the 1, and place it there.
Follow chains of signs
Signs that run in the same direction add up. In a row reading a < b < c, the first square is at most the grid size minus two, and the last is at least 3. A chain as long as the row fixes every square in it. Once a digit is placed, push its limits along the chain: if b is 4, a must be below 4 and c above it.
Use notes for the harder grids
Turn Notes on and pencil in the digits each square can still take. Placing a digit removes it from the notes in its row and column automatically.
Look for a digit that fits only one square in a row or column. That is where it goes, even if the square has other candidates.
On Expert, look for two squares in a line that can only hold the same two digits. Those digits can then be removed from every other square in that line.
Mistakes, hints and records
A digit repeated in a row or column turns red, and so does a sign that doesn’t hold, along with its squares. A sign also turns red when it can never hold, such as the largest digit on its small side.
Hint fills the selected square with its correct digit, or fixes a wrong digit elsewhere. Hints are counted for each puzzle.
Undo takes back any change. Your best time is kept for each difficulty, and the clock starts with your first move.