Coin problem
（重定向自Frobenius Number）
![With only 2 pence and 5 pence coins, one cannot make 3 pence, but one can make any higher amount.](/Images/godic/202501/14/Various_British_Pennys4710.JPG")
![Graphical solution of the Chicken McNuggets problem. The grid of points indicates that quantities that can be purchased are any positive multiple of 3 (with the exception of 3 itself) and any positive multiple of 20, as well as linear combinations thereof. Each sloping line x + y = k represents a total number of k nuggets. A red line goes through no grid points, so this number of nuggets cannot be purchased. A blue line goes through at least one grid point, so this number of nuggets can be purchased. The highest red line is x + y = 43.](/Images/godic/202501/14/Chicken_McNuggets_Problem_-_graphical_representation4710.jpg")
![McDonald's Chicken McNuggets in a box of 20.](/Images/godic/202501/14/Chicken_McNuggets4710.jpg")
The coin problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that asks for the largest monetary amount that cannot be obtained using only coins of specified denominations. For example, the largest amount that cannot be obtained using only coins of 3 and 5 units is 7 units. The solution to this problem for a given set of coin denominations is called the Frobenius number of the set.