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5 digit number

Posted on 2011-10-24
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Last Modified: 2012-05-12
Hi guys: Can any one please expain this question according to that answer ? Thanks.

A 5 digit number is formed according to the following rules:

The number contains only the digits 1,2,3,4 and these digits may be repeated or unused.

The first digit is 1.

If D1D2 are consecutive digits and D1 not equals to 4, then D1 < D2

If D1D2 are consecutive digits and D1 = 4, then D2 = 1.

(In other words, digits must be in increasing order, except that any 4 must followed by 1. For example, 12413 is one such number.) How many numbers of this type are there? Use a decision tree to compute your answer.

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Question by:mustish1
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TommySzalapski earned 1000 total points
ID: 37020845
You are supposed to find all possible 5 digit numbers that fit those rules.
The first digit has to be a one. Then each next digit can be either 2, 3, or 4.
Each next digit just has to be greater than the previous (and be from 1 to 4) unless the previous is 4 in which case the next is always two.

The tree is showing all the possible numbers. So if you trace the tree from the root (top) to any leaf node (on the bottom) and write down all the numbers you pass on the way down, you will get a 5 digit number that satisfies those rules. If you do that for each leaf node, you will get all of them.
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Expert Comment

by:TommySzalapski
ID: 37020855
If the problem did not include the tree, then you could easily build it yourself following the rules. Each node in the tree has nodes under it that represent digits allowed to follow that one.
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Author Comment

by:mustish1
ID: 37020904
Why these numbers are not in order like in the center the vertical line 1,3,4,1. Why its not 1,2,3,4
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Author Comment

by:mustish1
ID: 37021002
Also what does it means in the answer that there are 11 such numbers.
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Author Comment

by:mustish1
ID: 37021097
From the top node is 1 then it goes to 2, 3 and 4 on the left but why its not the same way on the right
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Assisted Solution

by:Saqib Husain, Syed
Saqib Husain, Syed earned 1000 total points
ID: 37021153
After 1 at the top there are three possibilities. It can be either 2 (left), 3 (middle) or 4 (right).

After this 2 there can be either 3 or 4 as shown

After the middle 3 there can be only a 4 which is shown.

After the left 4 there can be only a 1 which is shown.

This sequence follows and you get the tree shown above.

This tree shows all the different combinations possible which can be counted at the bottom line of the diagram.
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Author Comment

by:mustish1
ID: 37021166
k thanks. Just one last question why in  diagram it says that there are 11 such numbers.
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Expert Comment

by:Saqib Husain, Syed
ID: 37021172
Count the bottom ends
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