All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Tenacious Divisibility Treat (Posted on 2016-04-06) Difficulty: 2 of 5
A positive integer less than 30 million is such that if we subtract 5 from it – the resulting number is divisible by 8.

At the first step, from the number (considered originally) diminished by 5 - we subtract the eighth part. We then obtain a number that also becomes divisible by 8 after 5 is subtracted from it.

At the second step, we derive another in the same way, namely by subtracting a eighth part from the number at the end of the first step diminished by 5. The resulting number is also divisible by 8 after subtracting 5.

The operation concludes at 8th step given that at the end of 7th step we get a number that is divisible by 8 after after subtracting 5.

Determine the positive integer initially before the first step.

*** The resulting number at the end of 8th step is NOT necessarily divisible by 8 after subtracting 5.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
broll's interpretation is correct | Comment 8 of 9 |
Starting with broll's 16777181

 st = 16777181
 For rpt = 1 To 8
   newone = (st - 5) * 7 / 8
   Text1.Text = Text1.Text & newone & crlf
   st = newone
 Next

we do get a valid sequence: 

14680029 ... after first operation
12845021
11239389
9834461
8605149
7529501
6588309
5764766 ... after 8th operation

Starting with Ady's numbers:

From  11,983,725

10485755
9175031.25
8028147.96875
7024625.09765625
6146542.58544922
5378220.38726807
4705938.46385956
4117691.78087711


From  28,760,941
 
25165819
22020087.25
19267571.96875
16859121.0976563
14751726.5854492
12907756.3872681
11294282.4638596
9882492.78087711

all with non-integral values.

I believe Ady made the same mistake I made: dividing by 8 rather than multiplying by 7/8 at each step after subtracting 5.  I retracted that wrong solution. If one made that wrong choice, the one would indeed get

1497965
187245
23405
2925
365
45
5
0

or

3595117
449389
56173
7021
877
109
13
1

respectively.

  Posted by Charlie on 2016-04-07 10:41:07
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information