Math question

[ccyy1993]

If numbers are arranged in 3 rows A, B, C according to the following table, which row will contain the number 1000?

A:  1,  6,  7,  12,  13,  18,  19............

B:  2,  5,  8,  11,  14,  17,  20............

C:  3,  4,  9,  10,  15,  16,  21............

[smouse]

c

[smouse]

I see you had asked this before and wanted to know how to get it.

I used a spreadsheet you just choose one row and add 6 till you get near a thousand in this case 997 so 1000 must be on C

[Elf]

Ignore the rows that read upwards (4-5-6, 10-11-12 etc).  That leaves you with rows that look like this:

A: 1, 7, 13, 19

B: 2, 8, 14, 20

C: 3, 9, 15, 21

As the other respondent said, each row is the sequence of numbers you get by repeatedly adding 6.  So, if you take any number in a row and subtract the first number in that from it, the answer is divisible by 6.  For example, 19-1=18, 20-2=18, 21-3=18. 

To figure out which row a number would be in, therefore, the first step is to see if that number is divisible by 6 when you subtract 1, 2 or 3.

1000-1=999.  999/6=166.5

1000-2=998.  998/6=166.333

1000-3=997.  997/6=166.166

Because none of the results is exactly divisible by 6, we know that 1000 must be in one of the alternate rows - the ones that read upwards (like 4-5-6).  So, we look at 999 instead.

999-1=998.  We know that's not divisible by 6 (see above), so 999 can't be in row A, the row that starts with 1.

999-2=997.  We also know that's not divisible by 6, so 999 can't be in row B.

999-3=996.  996/6=166.  Aha!  999 must be in row C.

Now, we know that 999 in in row C, and 1000 is in a row that reads upwards and also that 1000 can't be in row B.  So, the row reading down must be 997-998-999 and 1000 is in the row following it that reads upwards (1000-1001-1002). 

A quick check on the row reading down to confirm:

997-1=996

998-2=996

999-3=996

[smouse]

wow thank heaven for spreadsheets and a bit of mental arithmetic!