Clearly A, B, and C are digits between zero and eight. A takes any value from 1 to 8.* There are thus eight possibilities for the value of A. Each value of A will dictate a value N, from 0 to 7, for (B+C). For a given value of N, B can take any value from 0 to N, and thus can take N + 1 different values, each corresponding to a particular value of C. So there are N + 1 ways of achieving (B+C) = N. The total number of combinations is therefore add up [N+1] between N=0 and N=7 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = (8 + 1) x 8/2 = 9 x 4 = 36 And here are those 36 solutions: 800,701,710,611,620,602,521,512,530,503,422,431,413,440,404,332,323,341,314,350,305,233,242,224,215,251,206,260,143,134,152,125,116,161,107,170 *If A was zero, we wouldn't really have a three digit number as required.
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Assuming you mean permutations of three digits, then the set of numbers that can be made with these digits is: 345 354 435 453 534 543 There are six possible permutations of three numbers.
Three digits.
All three numbers are significant digits, so 3.
21
Assuming that 001, 080, etc are not allowed (that is a leading zero or two is not permitted), the smallest number with exactly three digits is 100. The largest number with exactly three digits is 999. So there are 999 - 100 + 1 = 900 numbers with exactly three digits.