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        riddles >> easy >> A Weighty Problem
        
(Message started by: MpAdvisor on Feb 20^th, 2013, 8:39pm)

Title: A Weighty Problem
Post by MpAdvisor on Feb 20^th, 2013, 8:39pm

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?

Title: Re: A Weighty Problem
Post by pex on Feb 21^st, 2013, 2:28am

Looks like it can be done in ten different ways... any additional constraints?

[hideb]15+10 = 13+11+1 = 9+8+4+2+2
15+10 = 13+9+2+1 = 11+8+4+2
15+10 = 13+8+4 = 11+9+2+2+1
15+10 = 13+8+2+2 = 11+9+4+1
15+9+1 = 13+10+2 = 11+8+4+2
15+9+1 = 13+8+4 = 11+10+2+2
15+9+1 = 13+8+2+2 = 11+10+4
15+8+2 = 13+11+1 = 10+9+4+2
15+8+2 = 13+10+2 = 11+9+4+1
15+8+2 = 13+9+2+1 = 11+10+4[/hideb]

Title: Re: A Weighty Problem
Post by sc1ndy on Feb 25^th, 2013, 2:36am

[hide]11 + 9 + 4 + 1

13 + 2 + 10

15 + 8 + 2
[/hide]

You've added an extra 2kg.

Title: Re: A Weighty Problem
Post by pfeinstein on Feb 26^th, 2013, 3:37am

For example: [hide]
Crate 1:
15+9+1

Crate 2:
13+10+2

Crate 3:11+8+4+2[/hide]

But there are other ways too.

Title: Re: A Weighty Problem
Post by Jacob Black on Mar 12^th, 2013, 3:43am

The distribution can be as follows:
1st crate: 15kg + 9kg + 1kg
2ndcrate: 13kg + 10kg + 2kg
3rd crate: 11kg + 8kg + 2kg + 4kg
or
1st crate: 15kg + 10 kg
2ndcrate: 13kg + 9kg + 2kg + 1kg
3rd crate: 11kg + 8kg + 2kg + 4kg
0r
1st crate: 15kg + 8kg + 2kg
2ndcrate: 13kg + 9kg + 2kg + 1kg
3rd crate: 11kg +10kg + 4kg
etc

// spam link removed by moderator --SMQ

Title: Re: A Weighty Problem
Post by Apala on Mar 13^th, 2013, 12:35am

[hide]
{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}

[/hide] ::)

Title: Re: A Weighty Problem
Post by sanaya on Sep 3^rd, 2013, 1:52am

I find many different solutions some posted already by other members.

Title: Re: A Weighty Problem
Post by Grimbal on Oct 30^th, 2014, 1:30am

on 10/27/14 at 04:33:59, Annettagiles wrote:

In each crate you can load 25kgs

Another post by Annettagiles that doesn't make sense and got deleted.