#A40: Letter Weights

 This type brings back old memories of a puzzle book from Mindware called "Code Breakers" which was essentially systems of equations with the variables playfully disguised as colored circles. The key differences between these two ideas are that Letter Weights only uses addition but finds additional logic in requiring the solution be composed of a specific set of numbers, typically leading to logic vaguely reminiscent of Kakuro.

1. (1,2,3) ALLELE=10

2. (1,2,3,4,5) TEAMMATE=24, MATTER=17, MEET=9

3. (1,2,3,4,5,6) SIT=9, SLIT=12, SHEETS=26