+660 How many sets of four consecutive positive integers are there such that the product of the four integers is less than \(100,000\)?
Hint: Make sure you have a systematic way of keeping track of the items in your list.
Hint: The smallest set is [1, 2, 3, 4]. To find the largest set, use the fact that \(17^4≤100,000 ≤18^4.\) .
(n)(n + 1)(n + 2)(n + 3) =n^4 + 6 n^3 + 11 n^2 + 6 n
1 = 24
2 = 120
3 = 360
4 = 840
5 = 1680
6 = 3024
7 = 5040
8 = 7920
9 = 11880
10 = 17160
11 = 24024
12 = 32760
13 = 43680
14 = 57120
15 = 73440
16 = 93024
+37144 1234
2345
3456
4567
5678
6789
789 10
8 9 10 11
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16 17 18 19 looks like 16 sets to me
17 18 19 20 =116280 ==== too big
