A game has a solution with pure strategies if there is an element of the payoff matrix that is minimal in its row and maximal in its column. The value of the game is then the value of that element.

In the example in the spreadsheet, the element in row A2 and column B3 has that property.

An easy way to determine whether there is a solution with pure strategies is to circle the minimal element(s) in each row, and to put a square box round the maximal element(s) in each column. You then just have to look and see if there is an element that is both circled and boxed.