each of the students in a class writes a dirrerent 2 digit number on the whiteboard. the teacher claims that no matter what the students write, there will be at least three numbers on the whiteboard whose digits have the same sum. what is the smallest number of students in the class for the teacher to be correct?

I got the answer of 31 students. am i right? if i am not,could someone please show me how to figure this out?

Look at the sums:
ways to get sum of 1...10
ways to get sum of 2....20,11
How can three students get 3> 2,0;1,1, disallow 0,2
How can three students get 4> 4,0;22, 13, 31
get 5? 32, 23, 14, 41, 50
get 6 60, 51,15,24,42, 33
get 7 25, 16, 52, 61, 70, 43,34
get 8 17,71, 80, 62, 26, 35, 53,44
get 9 45, 54, 63,36, 27,72,`18,81,90
get 10 19,91,28,82,37,73,46,64, 55
get 11 29,92,38,83,74,47,56,65
notice the pattern...the ways to get a sum is always Sum until 9, then it is receeding in order.
get 12 ...7 ways (39,93,48,84,57,75, 66
get 13 six ways
get 14 five ways
get 15 four ways
get 16 three ways
get 17 two ways
get 18 one way.

Ok, then to have three in one sum, you will have two single sums, 15 of two sums, and one of three sums.

Number kids: 2 + 15*2 + 1*3

check my thinking.

  1. 👍
  2. 👎
  3. 👁
  1. 31 students

    1. 👍
    2. 👎
  2. In 18 ways get the sum from 1 to 18, I think if 3 students choose one any way of these sums, the teacher is correct. So the number of the students is 17x2+1x3=37

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Business Math

    Lee and Fred are elementary school teachers. Fred works for a charter school in Pacific Palisades, California, where class size reduction is a goal for 2013. Lee works for a noncharter school where funds do not allow for class

  2. math

    the ratio of the number of students in class A, B and C is 3:7:8. if 10 students leave c and join b , the ratio of the number of students in b and c would be reversed. find the total number of students in classes a,b and c Can I

  3. Mathematics

    A three digit number is such that twice the hundreds digit is more the teens digit by two.The unit digit is thrice the hundreds digit.When the digits are reversed the number is increased by 594.Find the number ?


    Aschool community had planned to reduce the number of agrade 10 students per class room by constructing additional class room. however,they constructed 4 less rooms than they aresult,the number of students per class was

  1. math

    students of class XI of a school were motivated to apply for NCC. from each section equal number of students opted for NCC. if there are 3x + 11 sections of class XI and total number of students in all the sections is represented

  2. Math

    Take a four digit number (abcd) and repeat it to make an eight digit number (abcdabcd). This eight-digit number always has at least three different prime factors, unless you start with a certain four-digit number. Which number is

  3. mathematics

    After 4 new students joined a class, the class had 32 students. Which equation can be used to find n, the number of students in the class before the 4 new students joined? A. n/4=32 B. n−4=32 C. 4n=32 D. n+4=32

  4. Mathematics

    The sum of the digits of a 3-digit number is three times the sum of the digits of a 2-digit number. When the 2-digit number is subtracted from the 3-digit number it gave another 2-digit number of which its first digit is three

  1. Math

    On a math test,12 students earned an A. This number is exactly 25% of the total number of students in the class. How many students are in the class? 'In this problem I'm not sure whether I'm being asked to solve for one or two

  2. algebra help!

    8) While eating in the cafeteria at school, 65%, or 26, of the students in the class ate pizza. find the number of students in the entire class. My guess is 17 students?? PlZ Help!

  3. algebra

    Classes A and B have 35 students each. If seven girls shift from class A to class B, then the number of girls in the classes would interchange. If four girls shift from class B to class A, then the number of girls in class A would

  4. math help!!!!! Thanks

    Eighteen students in a class play baseball. Seventeen students in the class play baseball. Thirty students in the class play either or both sports. In a Venn diagram which one shows the number of students who play basketball and

You can view more similar questions or ask a new question.