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

Home > Logic > Weights and Scales
Commemorations (Posted on 2013-02-06) Difficulty: 3 of 5
3 jealous brothers are to divvy up a set of commemorative coins.

There are an equal number of coins of each of the values: $1, $2, $3.

They discover that it is possible to do this in such a way that each brother gets a different assortment of coins, yet each gets the same number of coins and the same total value of coins.

What's the smallest possible number of coins in the set?

No Solution Yet Submitted by Jer    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
A misread? | Comment 4 of 7 |
 My reading of the problem was each brother got the the same value and the same number of coins but a different assortment across the range, ie, I saw all values as being represented in a person's allocation.
That latter thought however is not actually specified.  If that in fact was intended then one needs to look down the list to the rows beginning with 9.

Charlie does have such a line in his output.
Charlie's program does also allow for zero denominations (If my variables counted from zero I'd have a comparative output differing only by program structure).
        
      Person & Denomination
         A         B         C   
No|1  2  3| 1  2  3 |1  2  3
 3  1  1  1  1  1  1  1  1  1   6   6   6
 5  1  3  1  2  1  2  2  1  2  10  10  10
 5  2  1  2  1  3  1  2  1  2  10  10  10
 5  2  1  2  2  1  2  1  3  1  10  10  10
 6  2  2  2  2  2  2  2  2  2  12  12  12
 7  1  5  1  3  1  3  3  1  3  14  14  14
 7  2  3  2  2  3  2  3  1  3  14  14  14
 7  2  3  2  3  1  3  2  3  2  14  14  14
 7  3  1  3  1  5  1  3  1  3  14  14  14
 7  3  1  3  2  3  2  2  3  2  14  14  14
 7  3  1  3  3  1  3  1  5  1  14  14  14
 8  2  4  2  3  2  3  3  2  3  16  16  16
 8  3  2  3  2  4  2  3  2  3  16  16  16
 8  3  2  3  3  2  3  2  4  2  16  16  16
 9  1  7  1  4  1  4  4  1  4  18  18  18
 9  2  5  2  3  3  3  4  1  4  18  18  18
 9  2  5  2  4  1  4  3  3  3  18  18  18
 9  3  3  3  2  5  2  4  1  4  18  18  18
 9  3  3  3  3  3  3  3  3  3  18  18  18
 9  3  3  3  4  1  4  2  5  2  18  18  18
 9  4  1  4  1  7  1  4  1  4  18  18  18
 9  4  1  4  2  5  2  3  3  3  18  18  18
 9  4  1  4  3  3  3  2  5  2  18  18  18
 9  4  1  4  4  1  4  1  7  1  18  18  18


OPEN "c:\qb64\work\commems.txt" FOR OUTPUT AS #1

coins = 3
DO
 FOR a = 1 TO coins
  FOR b = 1 TO coins
   FOR c = 1 TO coins
    IF a + b + c = coins THEN
     FOR d = 1 TO coins
      FOR g = 1 TO coins
       IF a + d + g = coins THEN
        FOR e = 1 TO coins
         FOR f = 1 TO coins
          IF d + e + f = coins THEN
           FOR h = 1 TO coins
            IF b + e + h = coins THEN
             FOR i = 1 TO coins
              IF c + f + i = coins AND g + h + i = coins THEN
               p1 = a + b * 2 + c * 3
               p2 = d + e * 2 + f * 3
               p3 = g + h * 2 + i * 3
               IF p1 = p2 AND p1 = p3 AND p2 = p3 THEN

                PRINT coins; a; b; c; d; e; f; g; h; i; p1; p2; p3
                PRINT #1, coins; a; b; c; d; e; f; g; h; i; p1; p2; p3
               END IF
              END IF
             NEXT i
            END IF
           NEXT h
          END IF
         NEXT f
        NEXT e
       END IF
     NEXT g: NEXT d
    END IF
 NEXT c: NEXT b: NEXT a
 coins = coins + 1
LOOP WHILE coins <> 10

CLOSE 1


  Posted by brianjn on 2013-02-06 19:45:05
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 (2)
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