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Tim Kretschmer, 17, returned to his old school and, within minutes, left 10 students and three teachers dead.

1, Is 'old' correct? Shouldn't it be 'former' or 'previous'?

2. What is the reason for writing 'ten' as '10' and '3' as 'three'?  Is it correct to write ''3' instead of 'three'. Is there any rule for it?

Thanks.
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Hi,
Tim Kretschmer, 17, returned to his old school and, within minutes, left 10 students and three teachers dead.

1, Is 'old' correct? Shouldn't it be 'former' or 'previous'? 'Old' is OK. It's idiomatic, at least in British English.

2. What is the reason for writing 'ten' as '10' and '3' as 'three'? Is it correct to write ''3' instead of 'three'. Is there any rule for it? I forget the details of the so-called 'rule', but basically the idea is that small numbers should be written in words and big, awkward numbers should be written in 'digits'.
Newspapers and reporters often prefer digits. The use of both ways in this sentence is not good.

What a terrible event this was.

Best wishes, Clive
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In this context all three mean about the same thing but I think I prefer "old." I wish I could say why but the fact is it just "feels" right.

I prefer 'old' as well. Like 'the old stomping grounds' and such. Do 'former' and 'previous' imply that they have been replaced by a different school? Does 'old' make it more personal? Grabbing at straws here, since I'm sure no "rule" exists.
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Comments  
Lission1, Is 'old' correct? Shouldn't it be 'former' or 'previous'?
In this context all three mean about the same thing but I think I prefer "old." I wish I could say why but the fact is it just "feels" right.
Lission2. What is the reason for writing 'ten' as '10' and '3' as 'three'? Is it correct to write ''3' instead of 'three'. Is there any rule for it?
I would say it's carelessness on the author's part. With the exception of the age all of the numbers should have been written in words not digits. See this site for some guidance on this topic: http://owl.english.purdue.edu/handouts/esl/eslnumber.html
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PhilipDo 'former' and 'previous' imply that they have been replaced by a different school?
Bingo, now that you point it out it's obvious that that's what was bothering me.