A Weighty Problem Puzzle

### Author Topic: A Weighty Problem Puzzle  (Read 1900 times)

#### Masuma Parvin

• Sr. Member
• Posts: 323
##### A Weighty Problem Puzzle
« on: November 13, 2012, 04:09:13 PM »
A Weighty Problem
I have ten boxes which I want to pack into crates. Each crate can carry a maximum of 25 kg.

But I only have three crates, and the total weight of the boxes is 75kg:

15 kg, 13kg, 11 kg, 10 kg, 9 kg, 8 kg, 4 kg, 2 kg, 2kg, 1 kg

How can I pack the boxes into the crates?
The solution is:
Our Solution:

{Crate 1}, {Crate 2}, {Crate 3}
{15,10}, {13,8,4}, {11,9,2,2,1}
{15,10}, {13,11,1}, {9,8,4,2,2}
{15,10}, {11,8,4,2}, {13,9,2,1}
{15,10}, {11,9,4,1}, {13,8,2,2}
{11,10,4}, {15,8,2}, {13,9,2,1}
{11,10,4}, {15,9,1}, {13,8,2,2}
{13,8,4}, {15,9,1}, {11,10,2,2}
{13,10,2}, {15,8,2}, {11,9,4,1}
{13,10,2}, {15,9,1}, {11,8,4,2}
{13,11,1}, {15,8,2}, {10,9,4,2}

#### msu_math

• Jr. Member
• Posts: 81
##### Re: A Weighty Problem Puzzle
« Reply #1 on: November 13, 2012, 04:58:56 PM »
This inspection shows that there are 10 ways to pack the boxes into the crates. Is there any mathematical argument to prove that "no other ways are left to pack the boxes" ?

Lecturer in Mathematics
Department of Natural Sciences
FSIT, DIU