Rules
A number jumps as many squares as it says, across or up and down. A 1 reaches its neighbour, a 3 reaches three squares away. It jumps over anything in between, but must land on another number.
The smaller is taken from the larger, and the rest stays where it landed. Equal numbers both vanish. When a number gets smaller, its jump gets shorter.
Every level can be solved. The wrong order can leave numbers that cannot reach each other. Undo freely and try another way.
Clear a level without undoing to earn three stars. One or two undos earn two, more earn one. Starting over counts as one undo.
How to spot the traps
A number with no partner
Every number has to meet another one sooner or later. If it can no longer reach anything, and nothing can reach it, it is left behind. Watch for numbers about to be left alone in their row and column.
Two that need the same one
If two numbers can only be cleared by one and the same number, it must have enough for both. 5 can take 3 and then 2 (5 − 3 = 2, and 2 − 2 = 0), but 4 cannot manage both 3 and 2.
Even and odd
When two numbers meet, whether the sum of all the numbers is even or odd never changes. A board that can be cleared has an even sum, and so has every group of numbers that can never reach the others.
For more, the mathematics is in the paper: Read the paper (PDF).