## 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?]

*Answers to this challenge can be entered into the section below; submissions will automatically be revealed when time is up!*

RK| Founder | Profile March 30th, 2011 - 10:00 pmtest

Bobo The Bear| PUZZLE MASTER | Profile March 30th, 2011 - 11:20 pmThe 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.

suineg| PUZZLE MASTER | Profile March 31st, 2011 - 7:36 amThis 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!!

Shawn| PUZZLE GRANDMASTER | Profile March 31st, 2011 - 10:42 amI can get it down to 13/side

2

36

795

1840

Vik| Profile March 31st, 2011 - 11:24 am12

bizarette18| PUZZLE MASTER | Profile April 1st, 2011 - 3:57 am13

suropriya| Profile April 2nd, 2011 - 1:54 pmSmallest 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..

suropriya| Profile April 2nd, 2011 - 1:55 pm13 is the smallest such num ber..the pyramid has 0,1,2 in the vertices

Mashplum| PUZZLE MASTER | Profile April 2nd, 2011 - 7:16 pmIf 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

Hex| PUZZLE MASTER | Profile April 3rd, 2011 - 6:31 amSmallest is 13

…0

..7 3

.5 8

1 6 4 2

Jimmy Anders| PUZZLE MASTER | Profile April 16th, 2011 - 1:57 pmI’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…

kmn21| Profile April 18th, 2011 - 6:16 pm13 maybe????

2

36

795

1804

DanWebb| Profile October 9th, 2013 - 2:57 pm12