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        riddles >> hard >> Adding signs to make 100
        
(Message started by: elway on Nov 30^th, 2004, 1:21pm)

Title: Adding signs to make 100
Post by elway on Nov 30^th, 2004, 1:21pm

Ok, Here is a set of numbers:
1 2 3 4 5 6 7 8 9
You need to add plus and minus signs so that it equals 100. Here is one way to do it:
1+2+3-4+5+6+78+9=100
Can you help me find other ways?

Title: Re: This is driving me nuts!
Post by towr on Nov 30^th, 2004, 2:55pm

here's two
12+3+4+5-6-7+89 = 100
1+23-4+56+7+8+9 = 100

Title: Re: This is driving me nuts!
Post by elway on Nov 30^th, 2004, 3:00pm

thnx, is there any more?

Title: Re: This is driving me nuts!
Post by Grimbal on Nov 30^th, 2004, 3:03pm

Here are some:
1+2+3-4+5+6+78+9
1+2+34-5+67-8+9
1+23-4+5+6+78-9
1+23-4+56+7+8+9
-1+2-3+4+5+6+78+9
12+3+4+5-6-7+89
12+3-4+5+67+8+9
12-3-4+5-6+7+89
123-4-5-6-7+8-9
123+45-67+8-9
123-45-67+89

Title: Re: This is driving me nuts!
Post by Barukh on Dec 1^st, 2004, 1:07am

Although there are many, many more solutions, there are only 10 different types of solutions – w.r.t. how digits are partitioned into numbers:

1. 123, 45, 67, 89
2. 123, 4, 5, 67, 89
3. 123, 45, 67, 8, 9
4. 1, 2, 34, 5, 67, 8, 9
5. 1, 23, 4, 5, 6, 78, 9
6. 1, 23, 4, 56, 7, 8, 9
7. 12, 3, 4, 5, 6, 7, 89
8. 12, 3, 4, 5, 67, 8, 9
9. 123, 4, 5, 6, 7, 8, 9
10. 1, 2, 3, 4, 5, 6, 78, 9

All types but one (#2) were exemplified in previous posts. The remaining type has the following solution:

123 + 4 - 5 - 67 + 89 = 100

Another question: How many different types there exist if we reverse the order of digits?

Title: Re: This is driving me nuts!
Post by Grimbal on Dec 1^st, 2004, 12:22pm

1. 9 8 7 65 4 32 1
2. 9 8 76 5 4 3 2 1
3. 9 8 76 5 4 3 21
4. 9 8 76 5 43 2 1
5. 9 8 76 54 32 1
6. 98 7 6 5 4 3 2 1
7. 98 7 6 5 4 3 21
8. 98 76 54 3 21

Title: Re: Adding signs to make 100
Post by elway on Dec 3^rd, 2004, 1:16pm

can someone tell me how u get those so quickly, and like show work or something.

Title: Re: Adding signs to make 100
Post by Barukh on Dec 5^th, 2004, 11:41pm

on 12/03/04 at 13:16:35, elway wrote:

can someone tell me how u get those so quickly, and like show work or something.

In my case, there wasn’t too much cleverness: I once wrote a program for another thread (much more difficult problem), and now I am using it from time to time to solve this kind of questions. So, if you wish, it was one-time cleverness. ;D

To demonstrate, here’s a much tougher question:

With one additional constraint that the first number cannot be negative, find an ordering of digits 1 through 9 such that 100 cannot be achieved at all?

Title: Re: Adding signs to make 100
Post by Grimbal on Dec 6^th, 2004, 8:01am

In my case it was a small program I wrote from scratch.

I can post it if you are interested.

Title: Re: Adding signs to make 100
Post by krishna366 on May 14^th, 2005, 5:19am

This question was asked to me in ORACLE interview. My answer

1+2+3+4+5+6+7+(8*9)

i started from back.... 8*9=72. so i still require 28. then suddenly i got a thought that for every odd number u will have (n - 1)/2 combinations in [ 1, n-1] which sum up to n. SO i wrote

sigma(1 to 7)+pi(8 * 9) [Ya u have to write all these to impress ur interviewer.........