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avatar+642 

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 \(17^4≤100,000 ≤18^4.\) .

 Aug 10, 2023
 #3
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+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

 

 Aug 10, 2023
 #4
avatar+36899 
+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

 Aug 10, 2023

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