Some help needed

A

Aarna

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Sasha’s secret passcode is a nine-digit number that begins and ends with 6. The
sum of every three consecutive digits in the number is 14. What is the fifth digit
of Sasha’s passcode?

How would I solve this?
 
Aarna said:
Sasha’s secret passcode is a nine-digit number that begins and ends with 6. The
sum of every three consecutive digits in the number is 14. What is the fifth digit
of Sasha’s passcode?

How would I solve this?
Click to expand...
The first and ninth place is filled with 6. So there are 7 more spaces left to be filled with choices from 10 digits (0 - 9). Continue.....

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
Aarna said:
Sasha’s secret passcode is a nine-digit number that begins and ends with 6. The
sum of every three consecutive digits in the number is 14. What is the fifth digit
of Sasha’s passcode?

How would I solve this?
Click to expand...
I would start by just trying to make a passcode that fits the description, without deep thought, just to get a feel for how much freedom you have.

For example, you have 6 _ _ _ _ _ _ _ 6. Suppose you fill in the second digit with, say, 4. Is the third digit forced on you, or can you make another free choice? Keep going: 6 4 ? _ _ _ _ _ 6

What goes wrong?

To find an actual solution, if you've learned a little algebra, you might next try calling that second digit x: 6 x _ _ _ _ _ _ 6. Or, you could just try every possibility, and maybe discover something along the way.
 
Subhotosh Khan said:
The first and ninth place is filled with 6. So there are 7 more spaces left to be filled with choices from 10 digits (0 - 9). Continue.....

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
Click to expand...
6,3,5,5,4,9,1,7,6 this is what my answer was. But then I thought then can't the numbers be different every time the question is solved because you can use different combinations to make 14?
 
Dr.Peterson said:
I would start by just trying to make a passcode that fits the description, without deep thought, just to get a feel for how much freedom you have.

For example, you have 6 _ _ _ _ _ _ _ 6. Suppose you fill in the second digit with, say, 4. Is the third digit forced on you, or can you make another free choice? Keep going: 6 4 ? _ _ _ _ _ 6

What goes wrong?

To find an actual solution, if you've learned a little algebra, you might next try calling that second digit x: 6 x _ _ _ _ _ _ 6. Or, you could just try every possibility, and maybe discover something along the way.
Click to expand...
But even with algebra, couldn't the answers change every time because you can use different combinations to make 14?
 
Aarna said:
6,3,5,5,4,9,1,7,6 this is what my answer was. But then I thought then can't the numbers be different every time the question is solved because you can use different combinations to make 14?
Click to expand...
Aarna said:
The
sum of every three consecutive digits in the number is 14.
Click to expand...
In your example, what is the sum of 2 nd., 3 rd. & 4 th. digit? - not 14 !
 
Aarna said:
Oh! I get it, you must use simultaneous equations for this! Thank you!
Click to expand...
The approach I had in mind needs only one variable; you put this under Arithmetic, so I didn't know whether you could even use that. (Yes, it can be solved without algebra, by thinking about how addition works.) But this approach is ultimately equivalent.

And my expectation was that once you made an attempt and looked at it, you would realize that it didn't really fit the rules! (Unless you happened to make a lucky guess.) Trying a specific example is often important for understanding the meaning of a problem.
 
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