HotLicks has a valid answer, but I think an NSDictionary is a better solution. Create keys based on button presses, like:
@{ @"RedWhite" : @"Cow",
@"WhiteRed" : @"Chicken" };
Your code will be easier to read, and you can support three presses easily (assuming you're working with a timer that you invalidate after each press) by just adding another key; no recalculating your array:
@{ @"RedWhiteBlue" : @"America" };