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Sunday, January 27, 2008

Odd Arithmetic

Find four consecutive odd numbers that add up to 80.

Find five consecutive odd numbers that add up to 85.

5 comments:

Anonymous said...

17 + 19 + 21 + 23 = 80

13 + 15 + 17 + 19 + 21 =85

morris tao said...

Generic solution: Calculate the average value of each number and just pick equal odd numbers on both sides of that value.
For example 80/4 numbers = average value of 20 for each number

Picking 2 odd numbers below 20 and two above 20 gives you the solution.

Same idea for the other problem.

Math Genius 900 said...
This comment has been removed by the author.
Math Genius 900 said...

the easiest way to do these is to assign the lowest odd number the value of x.
that way all u have to do is solve
(x) + (x+2) + (x+4) + (x+6) = 80
4x + 12=80
4x=68
x=17

thus, the 4 numbers are 17,19,21,23
use the exact same process to find that the second question has the solution 13,15,17,19,21

Also, if you find that the value of x is an even number, that means the problem (in this case) would have no solution

Anonymous said...

actually, you can solve this problem even if you're not using algebra...

this is the easiest question in this site!