All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
Winning Ticket Tickle (Posted on 2014-10-06) Difficulty: 3 of 5
Gavin buys a lottery ticket, and in accordance with the rules he picks six different integers from through 1 to 46 inclusively. He chooses his numbers so that the sum of the base-ten logarithms of his six numbers is an integer.

By coincidence, the integers on the winning ticket have the same property - that is: the sum of the base-ten logarithms of the six numbers is an integer.

What is the probability that Gavin holds the winning ticket?

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts computer aided solution | Comment 3 of 6 |
There are 12 numbers that are either powers of 2, of 5 or a combination thereof between 1 and 45: 1, 2, 4, 8, 16, 32, 5, 25, 10, 20, 40, 50.

They can be multiplied in various combinations of six to produce a power of 10, and the following program finds these ways:

DefDbl A-Z
Dim crlf$, num(12)


Private Sub Form_Load()
 ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 
 DoEvents
 
 num(1) = 1
 num(2) = 2
 num(3) = 4
 num(4) = 8
 num(5) = 16
 num(6) = 32
 num(7) = 5
 num(8) = 25
 num(9) = 10
 num(10) = 20
 num(11) = 40
 num(12) = 50

For a = 1 To 7
For b = a + 1 To 8
For c = b + 1 To 9
For d = c + 1 To 10
For e = d + 1 To 11
For f = e + 1 To 12
   prod = num(a) * num(b) * num(c) * num(d) * num(e) * num(f)
   If prod = 10 Or prod = 100 Or prod = 1000 Or prod = 10000 Or prod = 100000 Or prod = 1000000 Or prod = 10000000 Or prod = 100000000 Then
    Text1.Text = Text1.Text & Str(num(a)) & Str(num(b)) & Str(num(c)) & Str(num(d)) & Str(num(e)) & Str(num(f))
    Text1.Text = Text1.Text & "     " & prod & crlf
    ct = ct + 1
   End If
Next
Next
Next
Next
Next
Next
 
 Text1.Text = Text1.Text & crlf & Str(ct) & " done"
End Sub


   numbers         product
 1 2 4 5 25 10     10000
 1 2 4 25 10 50     100000
 1 2 8 5 25 50     100000
 1 2 5 25 10 40     100000
 1 2 5 10 20 50     100000
 1 2 25 10 40 50     1000000
 1 4 5 25 10 20     100000
 1 4 5 25 40 50     1000000
 1 4 25 10 20 50     1000000
 1 8 5 25 20 50     1000000
 1 16 5 25 10 50     1000000
 1 5 25 10 20 40     1000000
 1 25 10 20 40 50     10000000
 2 4 5 25 20 50     1000000
 2 8 5 25 10 50     1000000
 2 5 25 20 40 50     10000000
 4 5 25 10 40 50     10000000
 8 5 25 10 20 50     10000000
 
There are 18 ways, so Gavin's probability of a win is 1/18


  Posted by Charlie on 2014-10-06 14:19:08
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information