Puzzle:
How many consecutive zeros are there at the end of 100! (100 factorial) ?
For Solution SCROLL DOWN...
Play Escape the Room Games.
Solution:
There are 24 zeros on the end of 100!
There are 24 zeros on the end of 100!
One solution would be to work this out and count the zeros, well I've done this so you don't have to. The answer is...
9332621544394415268169923885626670049071596826438162146859296389521759999322991560894146397615651828625369792082722375825118520916864000000000000000000000000Well now you can clearly just count the zeros but actually working out the number is not practical so we need another plan.
The clever bit here is thinking what numbers when multiplied together will end in a zero.
So the product of what numbers when multiplied ends in a zero:
1. When one of the things being multiplied ends in zero itself
2. A number ending in 5 multiplied by an even number
Below is tabulated the origin of all the zeros:
So that's it then there are 24 zeros at the end of 100!
The clever bit here is thinking what numbers when multiplied together will end in a zero.
So the product of what numbers when multiplied ends in a zero:
1. When one of the things being multiplied ends in zero itself
2. A number ending in 5 multiplied by an even number
3. 25, 50 and 75 when multiplied by some of the small numbers available eg (4, 2 and 6) generate an extra zero
Below is tabulated the origin of all the zeros:
| Number | Zeros | Number | Zeros |
| 100 | 2 | 95 | 1 |
| 90 | 1 | 85 | 1 |
| 80 | 1 | 75 | 2 |
| 70 | 1 | 65 | 1 |
| 60 | 1 | 55 | 1 |
| 50 | 2 | 45 | 1 |
| 40 | 1 | 35 | 1 |
| 30 | 1 | 25 | 2 |
| 20 | 1 | 15 | 1 |
| 10 | 1 | 5 | 1 |
| Total | 12 | Total | 12 |
So that's it then there are 24 zeros at the end of 100!
91 comments:
100->2
95 ->1
90->1
85->1
80->1
75->2
70->1
65->1
60->1
55->1
50->2
45->1
40->1
35->1
30->1
25->2
20->1
15->1
10->1
5-> 1
========
==> 24
24
100 TWO zeroes
from 20 to 90 add each one - EIGHT zeroes
unit's digit product 9.8.7...2.1 add to one each and hence - TEN zeroes
TOTAL OF TWENTY ZEROES
[100/5]+[100/25]
=20+4
=24
[100/5]+[100/25]
=20+4
=24
[100/5]+[100/25]
=20+4
=24
[100/5]+[100/25]
=20+4
=24
[100/5]+[100/25]
=20+4
=24
For any number result will be:
N/5 +N/25 + N/125 +N/625 +......
Taking integer part only.
hey satish .. ive to solve : the number of cosecutive zeroes in 2008 .. so i found ur ans.. but was wonderig where do i end the series.. if u cud reply back wud be great.. thanks
Suman,
Your solution seems to be correct.. but I have a doubt about this:
Why cant any number ending with 5 (other than 25, 75) lead to an extra 0, for example like 45, 65.. and so on.. I am not sure why this cant happen.
Can some body answer this ?
The reason is 25,50 and 75 contains the full square of 5 i.e. 25 = 5*5*1, 50=5*5*2, 75=5*5*3.
Hi everyone
I'm new to this forum.. Hope to have nice time around here...
Take care, Dennis from [url=http://www.myonlinepayday.com]Payday Loans[/url] website!
Good one.
hey dude there is one digit missing in your answer
the last digits of your answer is :
20916864000000000000000000000000
but the correct one is :
210916864000000000000000000000000
5! = 120
10 ! = ------- 00
15 ! = ------- 000
20 ! = ------- 0000
in short after every 5 one zero is added. There are 10 5's and 10 100's from 1 to 100 hence 100 ! has 20 Zero's
Niranjan
You need to go to 25!
Surprise 6 zeroes - Not 5
http://heraldbulletin.neighborsink.com/node/247694
http://archive.remdublin.com/blog/huangshumei/2013/01/28/end-spyware
http://bloggervillage.com/index.php?do=/blog/5026/costing-%C3%A2%C2%A335-on-a-12-month-plan-and-includes-%C3%A2%C2%A35-of-free-downloads/
http://17951501.at.webry.info/201301/article_33.html
http://www.clickprofesor.com/index.php?do=/blog/47656/when-you-use-a-spyware-remover/
http://www.chumclubs.com/blog/30651/having-too-many-spyware-remover-039-s-or-running-on-your-system-actually-co/
http://www.toma.jp/blog/aaa333/?entry_id=870947
http://hollar.se/index.php?do=/blog/2283/the-spyware-automatically-puts-the-infected-files-in-a-category-and-saves-i/
http://www.toma.jp/blog/jiumengshici/?entry_id=869830
http://demo.datastatic.com/jcow/index.php?p=blogs/viewstory/222
http://jiumengshici.hatenablog.com/entry/2013/01/28/145228
http://d.hatena.ne.jp/jiumengshici/20130128/1359352881
http://www.mymarburg.com/blog/76809/this-can-%E3%83%9F-%E3%83%A5-%E3%82%A6-%E3%83%9F-%E3%83%A5-%E3%82%A6-%E8%B2%A1-%E5%B8%83-be-even-more-true-if-you-use-refilled-ink-cartridg/
http://www.moselbook.de/index.php?p=blogs/viewstory/144331
http://jiumengshi.exblog.jp/17708619
http://thomsonshomebusiness.com/addons/socialnetwork2/index.php?p=blogs/viewstory/114
http://blog.qlep.com/blog.php/216559/718423
http://www.altasbaixarias.baumgarten.cnt.br/jcow/blogs/viewstory/87669
http://blog.yaolvyou.com/xmyshang/archive/13764.aspx
http://nen360.nenonline.org/blog/life-issues-pt-3-attitude-gratitude
http://nen360.nenonline.org/blog/always-be-aware-where-you-search-your-spybot-virus-protetion
http://www.webshare.cc/blog/b/blog_view.php?mid=547194&id=147&show_bbslink=
http://www.acdating.net/index.php?do=/blog/77202/payg-phones-with-no-hassles/
http://jiumengshi.exblog.jp/17708619
http://www.benches2swings.com/vocab/catpath/get-spybot-protection-spybot-can-take-control-your-pc.html-0
http://sns.cam111.com/blogs/entry/-The-pay-as-you-go-is-the-most-convenient-and-straightforward-modes-which-comes-without-any-hidden-or-the-monthly-fe
http://hollar.se/index.php?do=/blog/2283/the-spyware-automatically-puts-the-infected-files-in-a-category-and-saves-i/
http://jiumengshi.exblog.jp/17708624
http://bloggervillage.com/index.php?do=/blog/5081/the-on-tory-burch-riding-boots-foot-navigation-is-a-great-additional-featur/
http://thundernetworks.info/jcow/index.php?p=blogs/viewstory/28091
Do you mind if I quote a couple of your posts as
long as I provide credit and sources back to your webpage?
My blog is in the exact same niche as yours and my users would genuinely benefit from a lot of the information you present here.
Please let me know if this okay with you. Appreciate it!
Here is my web blog :: www.youtube.Com
Thanks so much for this. I'm a writer from Moirano, Italia and what I just read here on blogger.com could not be written any better. Going through this information reminds me of my past roomie, Garrett. He always kept preaching about this. I most certainly will send this stuff to him. Pretty sure he will have a very good read. I appreciate you for posting this.
my site ... cash for gold prices
Can I just say that after finding Blogger: Solve One Puzzle A
Day on Pimcore, what a comfort to uncover somebody who truly knows
what they're writing about on the web. You certainly realize how to bring a problem to light and make it worthwhile. A lot more people need to have a look at this and understand this perspective. It's surprising you're not more well-known, as you most certainly possess the gift.
my web page :: http://nepaliz.com/husabehlivu780
Hey there, my name is Adrienne and I'm a fellow blogger out of Wei�enhorn, Germany. I like what you guys are up to. Coming upon blogger.com was refreshing and helpful in terms of writing and work. Keep up the good work guys: I’ve put you guys on my blogroll. I think it will boost the value of my web site.
My web-site - chao
Hey there just wanted to give you a brief heads up and let you know a
few of the images aren't loading correctly. I'm not sure
why but I think its a linking issue. I've tried it in two different browsers and both show the same results.
my weblog www.cepaxarquia.org
We're a group of volunteers and opening a new scheme in our community. Your website provided us with helpful info to work on. You've done an impressive activity and our whole neighborhood will be grateful
to you.
Feel free to surf to my homepage - robe avocat
Wow that was unusual. I just wrote an really long comment but after I clicked submit my comment didn't show up. Grrrr... well I'm not writing all that over again.
Regardless, just wanted to say superb blog!
My blog post download 7Zip
Hi my friend! I want to say that this article is awesome, great written and
come with almost all significant infos. I would like to look more
posts like this .
Stop by my weblog - how to lose belly fat
Hurrah! In the end I got a webpage from where I can truly obtain
useful information regarding my study and knowledge.
Here is my page ... unknown
Hello there! Quick question that's totally off topic. Do you know how to make your site mobile friendly? My blog looks weird when browsing from my apple iphone. I'm trying to find a theme or plugin that might be able to fix this issue.
If you have any suggestions, please share. Thank you!
Here is my web blog; Unknown
What's Happening i am new to this, I stumbled upon this I have found It positively useful and it has aided me out loads. I am hoping to contribute & aid different customers like its aided me. Good job.
Feel free to surf to my website; ps3 jailbreak
Thanks for another informative site. Where else
may just I am getting that kind of info written in such an ideal approach?
I've a mission that I'm simply now working on, and I have been on the glance out
for such info.
Also visit my web-site :: jamieonei.autisable.com
Woah! I'm really loving the template/theme of this website. It's simple,
yet effective. A lot of times it's challenging to get that "perfect balance" between usability and visual appearance. I must say you have done a awesome job with this. In addition, the blog loads extremely quick for me on Safari. Excellent Blog!
Look at my homepage :: Unknown
hp laserjet 1020 motorists assists Windows 2000,
Windows XP, Vista and windows7(Home & Expert).
The HP 1020 LaserJet is an excellent.
Here is my homepage techniquench.wordpress.com
Pretty! This was a really wonderful post. Many thanks for providing these details.
Also visit my weblog ... pirater un compte facebook
Woah! I'm really enjoying the template/theme of this site. It's simple, yet effective.
A lot of times it's tough to get that "perfect balance" between user friendliness and visual appeal. I must say you've done a
excellent job with this. In addition, the blog loads extremely quick for me
on Safari. Superb Blog!
my web site ... xerox 8560mfp\/d
very intriguing, thanks a lot!
Feel free to visit my homepage - Www.bsansw.com
You're so awesome! I don't believe I've read anything like this before. So nice to find somebody with some original thoughts on this topic. Seriously.. thanks for starting this up. This website is one thing that is needed on the internet, someone with some originality!
Feel free to surf to my homepage; Buy Garcinia cambogis
Aw, this was an incredibly good post. Spending some time
and actual effort to generate a very good article… but what can I say… I procrastinate a whole lot and
never manage to get nearly anything done.
Also visit my website ... Psn Code Generator
Spot on with this write-up, I absolutely feel
this website needs much more attention. I'll probably be back again to read more, thanks for the information!
Look into my web site - xerox 8560dn printer
Good post. I learn something new and challenging on sites I stumbleupon every day.
It's always useful to read content from other authors and practice a little something from other websites.
My blog: ladies fashion jewellery
Back in the past days (definition: 10 years ago) printservers
would certainly often have their own collection of records
that would be appended to every printjob, essentially increasing the complication of the job.
That was at times adequate to make a device run out of memory.
I have no idea if it still makes much of a distinction nowadays.
Check out my web site; alwaysagirlygirl.blogspot.fr
Thanks a lot for vehicle drivers. really helpful website!
my web site: xerox phaser 8560n
These advantages (we counted 5) need to make you consider getting multi-function printers.
There are lots of printer brands online that offer advanced
attributes. So it's valuable if you seek for these multifunction printers on amazon, looked over evaluations and locate a low-cost multifunction printer for yourself.
+1.
my blog post ... xerox phaser 8560mfp driver
These are really impressive ideas in concerning blogging.
You have touched some nice things here. Any way keep up wrinting.
Also visit my blog post :: PS3 Jailbreak 4.41
You made some decent points there. I looked on the web for more info about the issue and found most individuals will go along with your views on this web site.
My page; microsoft office Gratuit
Hi all, here every one is sharing these kinds of know-how, thus it's nice to read this webpage, and I used to go to see this website everyday.
Also visit my homepage; recycling facts
Hello, There's no doubt that your website could possibly be having internet browser compatibility problems. Whenever I look at your website in Safari, it looks fine however, if opening in IE, it's got some
overlapping issues. I merely wanted to provide you with a
quick heads up! Aside from that, wonderful site!
My blog post http://journals.fotki.com/dar41444mc/liam-ballinger/entry/rwtbdkfqkfkd/
To be honest which is probably the greatest blogs I've read.
Also visit my web page ,Cheap costume earring Jewelry
Hi there everybody, here every person is sharing such experience, thus it's fastidious to read this web site, and I used to pay a visit this blog everyday.
Here is my site - Ps Jailbreak
A fascinating discussion is worth comment. There's no doubt that that you need to publish more about this subject, it might not be a taboo subject but usually people do not discuss these subjects. To the next! Kind regards!!
my weblog ... youtube.Com
I'm excited to discover this page. I wanted to thank you for your time due to this wonderful read!! I definitely savored every bit of it and i also have you saved as a favorite to look at new stuff in your site.
Here is my web-site; Candy crush saga hack
Thanks to my father who stated to me about this blog, this webpage is genuinely amazing.
Review my weblog: Psn Code Generator
I am regular visitor, how are you everybody?
This article posted at this web page is in fact good.
Look at my webpage :: Hultquist swarovski jewellery
Wow so amazing
Check out my blog ... http://www.toodbook.com/index.php?do=/blog/3465/jewellery-coming-from-the-danon-company/
Complication resolve with Samsung ML-1520 on WIN 8 Pro 64 little
bit.
Thanks to you !!!!!!
Great !!!!!!
Feel free to visit my homepage xerox phaser 8560 review
Hurrah, that's what I was looking for, what a stuff! existing here at this blog, thanks admin of this web page.
Feel free to surf to my blog: Generateur de Code PSN
Very nice post. I just stumbled upon your blog and wished to say that I've truly enjoyed surfing around your blog posts. In any case I will be subscribing to your rss feed and I hope you write again soon!
Also visit my web page ... xerox phaser 8560 service manual
When someone writes an paragraph he/she retains the plan of a user in his/her
brain that how a user can understand it. Thus that's why this post is great. Thanks!
Feel free to surf to my blog; Private Cloud Computing
No way to alphabetize after you configuration the
preliminary labels, yet it is extremely quick to make use of Ctrl+F (find function) to promptly locate a label to modify or get rid of
from your list. Good luck!
Here is my blog: shipin.yylearn.com
"It's like an reopen arena where most people can get anything fake. Made wristbands are smaller amount of expensive than debossed and embossed wristbands. May be you a hobbyist or opt that would settle for a single replica gucci bags?? Yes, you can have as many of their own kids as you desire. http://apbt.online-pedigrees.com/modules.php?name=Your_Account&op=userinfo&username=KarolinEU
my web site ... cheap gucci
Clive Parkin said on August 14, 2012
Also visit my website ... Danon jewellery england
GREAT !!!!!!!!!! Made my day !!!!!!!
Stop by my homepage - xerox phaser 8560mfp
Thanks a lot so much! Concerning just started making jewelry and this also basic step has not been explained
better!
Also visit my homepage; ,online jewellery deals
I would certainly cherish it highly if you would send
me an e-mail content of Make PCB making use of
a laser printer. Additionally, if readily available, I would certainly like to have any of the write-up pointed out in your
post. Thanks !!
Feel free to surf to my web-site; xerox phaser 8560n (e-diocese31.cef.fr)
I'm extremely impressed with your writing skills as well as with the layout on your blog. Is this a paid theme or did you customize it yourself? Anyway keep up the excellent quality writing, it is rare to see a nice blog like this one today.
My blog :: world Of tanks hack
The Victorians certainly got happy when they were depressed.
Pearls symbolising tears? Oh dear!
Also visit my webpage: danon jewellery uk
Excellent website. Lots of useful information here. I'm sending it to some buddies ans also sharing in delicious. And naturally, thanks for your sweat!
My web page; d�pannage volet roulant compact pas cher
If some one wants expert view concerning blogging and site-building
afterward i suggest him/her to go to see this blog,
Keep up the fastidious job.
My webpage: coffre fort Bricard dépannage pas cher
I read this post fully about the resemblance of most up-to-date and previous technologies, it's amazing article.
Feel free to visit my website: Vourtimera
Have you ever considered about including a little bit more than just your articles?
I mean, what you say is important and all.
Nevertheless imagine if you added some great graphics or
videos to give your posts more, "pop"! Your content is excellent but with pics and videos, this site could certainly be one of the very best in its
niche. Terrific blog!
Feel free to surf to my site :: Minecraft Gift Code Generator
Magnificent website. A lot of useful info here.
I'm sending it to a few friends ans additionally sharing in delicious. And naturally, thank you to your effort!
Have a look at my web blog; pilgrim jewellery ireland :: ali2s0nhbo.modwedding.com ::
Searching for Christmas gifts with teens may stay rather troubling.
During authentic boots, the letters will more or less overlap each several more.
Ugg boots are some of the most comfortable boots on the target audience today.
And jackets with long sleeves can help you to visually make your hands more refined.
http://mykharis.com/blog/view/97425/attraction-of-ugg-bottillons
Stuff with paper towels and dry faraway from heat and special sunshine.
For those who prefer our own adventurous side concerning fashion, leather and then lace always match.
This particular Classic Short, this important is one of ugg boots traditional designs.
Fringing and fur trim designed uggs could be a nice method to wear with rather
long winter skirts. http://www.compensation.ru/forum/profile.
php?id=59934
Great article, exactly what I was looking for.
Here is my web page - serrurier
Remarkable! Its in fact awesome paragraph, I have got much clear idea about from this post.
Here is my web site dé
I have read so many posts on the topic of the blogger lovers however this article is in fact
a pleasant post, keep it up.
Feel free to surf to my website - Acheter Coffre Fort NuméRique
Thanks very interesting blog!
my web blog: Webseite
Every weekend i used to pay a visit this
web site, as i wish for enjoyment, for the reason that this this web site conations in fact nice funny data too.
Look at my homepage - Minecraft Crack
Thanks for one's marvelous posting! I certainly enjoyed reading it, you're a great author.
I will always bookmark your blog and will eventually come back later in
life. I want to encourage one to continue your great work, have a nice holiday
weekend!
Feel free to visit my blog post: hultquist earrings
you are so scorching.
My homepage ... xerox phaser 8560 driver
It functions! And that's really nice that you uploaded this info ... I can easily not point out the same for Samsung who is suggesting something they did not examination!
Satisfied new year!
My web page Xerox Phaser 8560 Drivers
Attractive a part of content. I recently found your web site plus
accession capital to assert that we get in fact enjoyed account your website
posts. Anyway I'm going to be subscribing on your feeds and in many cases I achievement you access consistently fast.
My website; danon jewellery stockists
Good post! We will be linking to this great post on our website.
Keep up the good writing.
Here is my web site: xerox 8560 toner
Hi there, I do believe your website could be having web browser compatibility
problems. When I take a look at your web site in Safari, it looks fine but when
opening in Internet Explorer, it's got some overlapping issues. I merely wanted to give you a quick heads up! Other than that, excellent site!
Feel free to visit my website ... rosacea
Sir, very v usefull the website deliver me theVideo
thangs.
Stop by my website ... xerox phaser 8560 maintenance kit
I'm not sure where you are getting your information, however great topic. I needs to spend some time studying more or understanding more. Thank you for magnificent info I used to be searching for this information for my mission.
my weblog ... pilgrim jewellery denmark
The all circuit in this sites is extremely intereting i try it Im likewise a
B. e(electronic devices)pupil this website is truly great.
my page - xerox phaser 8560 maintenance kit (blartz.com)
Instead we can calculate it using, ceil(100/5)+ceil(100/(5^2)+ceil(100/5^3) = 24 :)
Here's a simple math puzzle that forces you to avoid brute force in solving it and instead look for different ways of thinking about the problem.
I thought about which numbers, when multiplied, will give you zeros. There's two types: numbers that end in zero (10, 20, etc...) and numbers that end in 5 (when they're multiplied by an even number!).
Counting all that, you get 21 zeros. But we're not done yet!
There are three instances where you end up with a number that ends in a five, then a zero (for example, I got 150, 50, and 1350 but this was specific for the numbers I multiplied to give me a better illustration of the zeros).
If you multiply these numbers by even numbers, you get one more zero (50 * 2 = 100, 150 * 4 = 600, etc..)
Therefore, there are 24 zeros at the end of 100!
I wonder if you could cleverly figure out what the digit would be right before the zeros started? It must be an even number because it's multiplied by 2, but I wonder if you could circumvent the process of actually solving 100! to find it. THAT would also be a good puzzle.
It's so simple you guy's are making it tough..................XD
simply divide the 100/5=20
Now divide the 20/5=4
Now add 20+4=24 Got Answer XD...........
Let me explain...........
Number of trailing zero are possible in only two case either in 2 or 5.
But 2 have less number of repetition or power as compare to 5.
So take 5 and divide the factorial number unless your remainder is less than the divisor.....
If you want to make it more clear then watch Rakesh Yadav Publication Videos on youtube...
We are Indian..............XD
Post a Comment