School-Safe Puzzle Games

Blue Paint Drums

A paint store was showcasing it’s new cobalt blue paint. Each paint drum, except one, was numbered as above. A boy passing the formation noticed that each side of the pyramid has numbers that add up to 16. Impressed by the boy’s observational skills, the store owner says he’ll reward the boy with a free paintbrush if he can figure out how to re-arrange the drums so that the three pyramid sides sum to the smallest possible number.

[in other words, all 3 sides have to add up to the same number. What is the smallest such number?]

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13 Comments to “Blue Paint Drums”


  1. RK | Founder | Profile

    test


  2. Bobo The Bear | PUZZLE MASTER | Profile

    The key is to minimize the 3 corners and maximize the center value.
    Placing 0, 1, 2 at the corners and 9 in the center, it’s easy to place the rest.
    One arrangement is:
    0
    8 5
    4 9 6
    1 3 7 2
    Any such arrangement will have sides adding up tp 13, which is the minimum.


  3. suineg | PUZZLE MASTER | Profile

    This puzzle is very very cool!!!, I think I came out with a kind of mathematical solution to it here it is:


    A,B,C are the extremes of each side, X is the sum of the two middle elements of side AB
    Y is the sum of the middle elements of side BC and Z is the sum of the middle elements of side AC, O is the center of the pyramid, R is the sum of the numbers in any side.


    Equations:
    1) A+B+C+X+Y+Z+O= 45 (THE SUM OF ALL THE NUMBERS FROM 0 TO 9)
    2) A+B+X= R
    3) A+C+Y= R
    4) B+C+Z= R


    NOW SUM 2,3,4:
    5)A+B+C+X+Y+Z+A+B+C=3R
    SUBSTITUTE 1 IN 5:
    6)A+B+C+45-0=3R –: A+B+C= 3R+O-45
    BUT YOU KNOW FROM THE NUMBERS GIVEN THAT A+B+C MORE OR EQUAL TO 3 SO
    3R+O-45 MORE OR EQUAL TO 3, TO MINIMIZE R YOU LOOK FOR THE GREATER O SO LETS ASSUME O = 9
    IF O=9, R MORE OR EQUAL TO 13, LETS PUT A,B,C : 1,2,0
    SIDE AB= 1,7,3,2= 13
    SIDE BC= 2,6,5,0= 13
    SIDE AC= 1,8,4,0= 13
    the minimum size is 13!, cool!!


  4. Shawn | PUZZLE GRANDMASTER | Profile

    I can get it down to 13/side


    2
    36
    795
    1840


  5. suropriya | Profile

    Smallest number is 13..with 0,1,2 in the three vertices and 4,8 between 0&1, 3,7 between 1&2 and 5,6 between 0&2 respectively..


  6. suropriya | Profile

    13 is the smallest such num ber..the pyramid has 0,1,2 in the vertices


  7. Mashplum | PUZZLE MASTER | Profile

    If you exclude the 9 by placing it in the middle, and put the blank, 1, and 2 at the vertices, so that only the smallest values will be used more than once, you can get sides that total 13.


    0
    86
    495
    1372


  8. Hex | PUZZLE MASTER | Profile

    Smallest is 13
    …0
    ..7 3
    .5 8
    1 6 4 2


  9. Jimmy Anders | PUZZLE MASTER | Profile

    I’ve worked in a paint store, and never did we stack our paint in such a way! (we always put the flat part on the bottom)
    I don’t think any of our customers would’ve earned the paintbrush either…


  10. kmn21 | Profile

    13 maybe????
    2
    36
    795
    1804


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