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 \(17^4≤100,000 ≤18^4.\) .

Keihaku Aug 10, 2023

#3**+2 **

(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**

Guest Aug 10, 2023

#4**+2 **

1234

2345

3456

4567

5678

6789

789 10

8 9 10 11

.

.

.

16 17 18 19 looks like 16 sets to me

17 18 19 20 =116280 ==== too big

ElectricPavlov Aug 10, 2023