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

Guest Jun 13, 2017

#1**+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.

004

013 103

022 112 202

031 121 211 301

040 130 220 310 400

I count fifteen of them.

hectictar
Jun 13, 2017

#2**+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

Melody
Jun 13, 2017

#3**+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.

TheXSquaredFactor
Jun 13, 2017