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pythagoras123
Group Title
The product of n whole numbers
1 x 2 x 3 x 4 x ... x (n1) x n, has twentyeight consecutive zeros. Find the largest value of n.
 2 years ago
 2 years ago
pythagoras123 Group Title
The product of n whole numbers 1 x 2 x 3 x 4 x ... x (n1) x n, has twentyeight consecutive zeros. Find the largest value of n.
 2 years ago
 2 years ago

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experimentX Group TitleBest ResponseYou've already chosen the best response.0
what are zeros??
 2 years ago

pythagoras123 Group TitleBest ResponseYou've already chosen the best response.0
"0". This is a zero. Consecutive zeros are zeros that appear consecutively, i.e. The product of 10 x 10x 10 has 3 consecutive zeros (1ooo)
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
It's somewhat tedious to explain the whole thing. One interesting observation is there would be only trailing zeroes.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
@ffm i'll try before you
 2 years ago

pythagoras123 Group TitleBest ResponseYou've already chosen the best response.0
Just tell me how you work it out, or the solution/methodology. The answer is not so important.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
i think between 1 and 10, you will have 2 zeros.
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
I have used binary search along with the usual De Polignac's formula (just) twice to yield 124 as the answer. Ref: http://en.wikipedia.org/wiki/De_Polignac%27s_formula
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
"Consecutive zeros are zeros that appear consecutively, i.e. The product of 10 x 10x 10 has 3 consecutive zeros (1ooo)" You haven't understood the problem.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
sorry, 139
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
@ffm is it correct??
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
33 for 139.
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
I have posted the correct answer.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
ah ... where did i screwed up??
 2 years ago

pythagoras123 Group TitleBest ResponseYou've already chosen the best response.0
@FoolforMath, how did you manage to get 124?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
looks like my theory screwed up from here http://www.wolframalpha.com/input/?i=30%21%2F20%21&dataset=&equal=Submit
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
3 zeros ,,,?? how 25*22 = 00 => two zeros were coming from here. so all the factors of 100 or 1000 or 10000 ... were causing problem for my idea.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
110 : 2 zeros 1020: 2 2030: 3 (25 is factor of 100) 3040: 2 4050: 3 (50 is factor of 100) 6060: 2 6070: 2 7080: 3 (at some point 75 will give two zeros) 8090: 2 90100: 3 (100 itself gives two)  so from 0 to 100 we have: 24 zeros 100110: 2 110120: 2  I guess that would give 28 zeros screw you > minions of 100
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
the answer was n = 120
 2 years ago

Aron_West Group TitleBest ResponseYou've already chosen the best response.0
The largest power of 5 dividing n must be 5^28.Now use De Polignac's Formula.
 2 years ago

eliassaab Group TitleBest ResponseYou've already chosen the best response.1
120! = 6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000 Of course you need an analytic proof of that using 2 and 5.
 2 years ago

eliassaab Group TitleBest ResponseYou've already chosen the best response.1
Should the question be, find the smallest n to achieve that?
 2 years ago
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