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A textbook has 1,000 pages. How many of the pages have page numbers whose digits add up to exactly 4?

 Jun 13, 2017
 #1
avatar+7352 
+3

This probably isn't the "smartest" method, but I just wrote them all out here.

I noticed that they follow a kind of pattern.   smiley

 

004

013     103

022     112     202

031     121     211     301

040     130     220     310     400

 

I count fifteen of  them.

 Jun 13, 2017
 #2
avatar+99384 
+3

That is a good method Hectictar, I just want to take a look too :)

 

400 any order      3                       The 4 can be 1st , 2nd or 3rd.

310 any order      3*2=6 ways      these pages are   13,31,103,130,301,310

211 any order      3

220 any order      3 ways    

 

                          15 ways          WE agree    laugh

 Jun 13, 2017
 #3
avatar+2340 
+1

Well, you can immediately eliminate the possibility of any of the digits being 5,6,7,8, or 9 because that would result in a sum greater than 4, which simplifies the problem somewhat.

 Jun 13, 2017

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