USA | A nice factorial equation | math Olympiad problem

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[ptsPeterSzabo]

It's a product of 4 consecutive integers. It may not contain 10, because 3024 doesn't end with 0. Thus it may be at least 14*13*12*11>10000 (too large) or at most 9*8*7*6. Bingo! 9*8*7*6 = 3024. Thus n+5 = 9, thus n = 4. This is hardly a math olypiad problem, it's much simpler.

[cianchetto]

bro WTF just factorialize 3024, since we know it must be a product of 4 consecutive numbers, as shown at 1:48, we have 3024=2^4 * 3^3 * 7. We can then easily see that the numbers are 6, 7, 8, 9 and therefore n=4

[radialwellendichtrin]

If you assume that n is a positive integer, take the 4th root of 3024 to get an estimate of the range for the values of (n+2), (n+3), (n+4) and (n+5). Then plug in a few integers and you'll have the solution much faster

[anantamurthy]

In this sum since 3+0+2+4 is 9
It is obvious it has to be 9*8*7*6 so on since 10 and above 10 are ruled out

[OriginalNoober]

without watching the video i just guessed from the 24 that maybe there's an eight in the mix, so i tried to find 4 consecutive numbers (including 8) that multiply to 3024, which after a failed try was 6x7x8x9

[Quest]

Its very east to get n=4 from making factors r. H. S n then equate ... No need to solve

[fuerdichundmich]

3024~10*10*10*3 but 10 is not part of the solution, because the last digit of 3024 isn‘t zero. Because the solution consist of 4 konsecutive integers and the closest product of integers to 10*10*10*3 that fullfills these conditions is 6*7*8*9 which is the solution.

[ayi_oglu_ayi]

part after 1:51 was pretty unnecessary, 3024 has 7 as a denominator and since its a prime, it must be one of the factors on the left side of the equation

[tinchote]

The solution looks too complicated. You have that 3024=2^4x3^3x7. I we postulate that one of the integers is 7, we see that trying with 7, 8, 9 what remains is 2x3=6, so the four numbers are 6, 7, 8, 9 and so n+2=6 and n=4.