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What The Code Puzzle - 18 June A man desired to get into his work building, however he had forgotten his code. However, he did recollect five pieces of information * Fifth number + Third number = 14 * The fourth number is one more than the second number. * The first number is one less than twice the second number. * The second number and the third number equals 10. * The sum of all five numbers is 30. What is the code ? For Solution : Click Here

 Aug 15, 2015

Best Answer 

 #4
avatar+101369 
+10

Let a, b, c, d and e be the digits in that order...so,we have the following system:  

 

c + e = 14  

d - b  = 1

2b - a = 1 

b + c = 10

a + b + c + d + e  = 30    (5)

 

Notice that 

c + e = 14

c + b = 10      subtracting the second equation from the first, we have

 

e - b = 4    → e = b + 4

 

And c = 10 - b

And d = 1 + b

And a = 2b - 1

 

And substituting all these into equation (5), we have

 

(2b - 1) + b + (10 - b) + (1 + b) + (b + 4) = 30    simplify

 

4b + 14 = 30     subtract 14 from each side

 

4b = 16  → b = 4

 

Then

 

c = 10 - 4 = 6

d = 1 + 4 = 5

e = 4 + 4  = 8

a = 2(4) - 1 = 7

 

And the code is:

 

abcde = 74658

 

Just as Anonymous found!!!!!

 

 

 

  

 Aug 15, 2015
 #1
avatar+101768 
+5

Was that supposed to be a hyperlink to the answer Maia?

 Aug 15, 2015
 #2
avatar+414 
+5

Yeah but It does not work bcz I pasted the question

 Aug 15, 2015
 #3
avatar
+5

I did it!! 74658

 Aug 15, 2015
 #4
avatar+101369 
+10
Best Answer

Let a, b, c, d and e be the digits in that order...so,we have the following system:  

 

c + e = 14  

d - b  = 1

2b - a = 1 

b + c = 10

a + b + c + d + e  = 30    (5)

 

Notice that 

c + e = 14

c + b = 10      subtracting the second equation from the first, we have

 

e - b = 4    → e = b + 4

 

And c = 10 - b

And d = 1 + b

And a = 2b - 1

 

And substituting all these into equation (5), we have

 

(2b - 1) + b + (10 - b) + (1 + b) + (b + 4) = 30    simplify

 

4b + 14 = 30     subtract 14 from each side

 

4b = 16  → b = 4

 

Then

 

c = 10 - 4 = 6

d = 1 + 4 = 5

e = 4 + 4  = 8

a = 2(4) - 1 = 7

 

And the code is:

 

abcde = 74658

 

Just as Anonymous found!!!!!

 

 

 

  

CPhill Aug 15, 2015

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