Multiple Sums

  1. There are 12 different ways you can add two numbers, between 1 and 25, to total 25: (1+24, 2+23, ..., 12+13). No number is used more than once. How many different combinations using 3 numbers to total 25 are there? Remember, use the numbers only once for each grouping. (i.e. 25 = 1+2+22 = 1+4+20 = 2+4+19, but not 1+12+12)
  2. Can you fill a table for the number of possible sums for totals from 20 to 30, with the number of terms in each sum from 2 to 7? Can you find a formula which would provide the answer for the number of possible sums of N, with k terms in each sum?
Source: Mind Bending Puzzles Calendar, Terry Stickles, January 14, 2000.
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