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2nd grade math (Posted on 2017-01-12) Difficulty: 3 of 5
My son is doing a math worksheet. He is practicing the concept of 'carrying' when doing sums. The sheet has 16 problems, each is summing two three-digit numbers. What struck me as interesting was that the creator of the problems made every problem have at least two carries and most have three.

What is the probability distribution for the number of carries in finding the sum of two randomly selected three-digit numbers?

Feel free to generalize.

No Solution Yet Submitted by Jer    
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re: solution -- simulation verification | Comment 2 of 4 |
(In reply to solution by Charlie)

DefDbl A-Z
Dim crlf$, ct(3)


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 mxtr = 1000000
 For tr = 1 To mxtr
   DoEvents
   r1 = Int(Rnd(1) * 900) + 100
   r2 = Int(Rnd(1) * 900) + 100
   a1$ = LTrim(Str(r1))
   a2$ = LTrim(Str(r2))
   carryCt = 0: carry = 0
   For p = 3 To 1 Step -1
     d1 = Val(Mid(a1, p, 1))
     d2 = Val(Mid(a2, p, 1))
     s = d1 + d2 + carry
     If s > 9 Then carry = 1: carryCt = carryCt + 1 Else carry = 0
   Next
   ct(carryCt) = ct(carryCt) + 1
 Next tr
 
 For c = 0 To 3
   Text1.Text = Text1.Text & Str(ct(c))
 Next
 Text1.Text = Text1.Text & crlf
  
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub


produces

 134550 342975 360366 162109

for counts of 0, 1, 2 or 3 carries adding two 3-digit numbers.

  Posted by Charlie on 2017-01-12 21:38:09
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