Zeros are not always easy

Number Theory Level 4

How many zeros are in the expansion of

$1^1 \times 2^2 \times 3^3 \times 4^4 \ldots \ldots \ldots \ldots \times 100^{100} ?$

The question asks for trailing zeros.

The answer is 1300.

1 solution

Rama Devi
Jun 3, 2015

Please up vote if you like my solution.

Moderator note:

Why the number of zeros will be equal to the power of 5?

What do you mean by zeros? 1000100 has 2 zeros or 5 zeros? You need to specify that in your question.

In response to challenge master note:Thanks , I have changed the question.

Rama Devi - 6 years ago

I also did the same way.

Ankit Raj - 6 years ago

Then why don't you up vote it.

Rama Devi - 6 years ago

I have upvoted it

Ankit Raj - 6 years ago

Also try my new set Number theory and combinatorics practise

Rama Devi - 6 years ago

@Rama Devi – I found no new set

Ankit Raj - 6 years ago

@Ankit Raj – You will surely find it.

Go to my profile and click on my set.

Follow me for more such problems.

Rama Devi - 6 years ago

@Ankit Raj – Are you trying it?

How did you feel ?

Rama Devi - 6 years ago

Well in your set combinatorics and nt practice there is a question about can we form 2 squares and 5 triangles with 8 lines. Its answer is no but it should be yes just draw a square using 4 lines. Draw its diagonals using 2 more lines . mark the square ABCD and intersection of diagonals at P now construct a right angled isosceles with hypotenuse AB and the third vertex above AB exactly at the mirror image of P say Q . So we get two squares ABCD and PAQB. And 5 right angled triangles APB , APC , BPC , BPD and AQB with only 8 lines. Iost my rating - :( . Plz repost it as a new problem

akash deep - 6 years ago

It is possible to make 2 squares and 4 triangles by using 8 lines but 5 triangles is not possible

Rama Devi - 6 years ago

You can just try what i have posted and you will get 5 small triangles as i have written please look at it once again

akash deep - 6 years ago

@Akash Deep – I already tried it.I don't think that it is possible.

Rama Devi - 6 years ago

@Rama Devi – it is possible. just like adding an extra triangle(of equal area)to any side of d first square. that on its own fkrm a square with the closest triangle.

Joseph Eze - 5 years, 11 months ago

Zeros are not always easy

The answer is 1300.

1 solution

Moderator note:

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