Problem
COM-B1-M06-P020 Cells with Coordinates
#20
★★★☆☆ Level 3 of 5
A token starts at cell \((0,0)\). In one move it may go to \((x+2,y+1)\) or \((x+1,y+2)\). Can it reach \((10,10)\)?
Look at the sum of coordinates modulo \(3\).
Each move increases \(x+y\) by \(3\). Thus \(x+y\) modulo \(3\) is preserved and equals \(0\). At \((10,10)\), the coordinate sum is \(20\equiv2\pmod3\). It cannot be reached.
Coordinate modular invariant.