Math Is Fun Forum

shocamefromebay

Member

Registered: 2007-05-30

Posts: 103

Drawing the line.

You start with zero. you must add or subtract each and every number between one thru nine. which numbers must you add or subtract to get 16 when adding or subtracting all the numbers??

Heres the

Last edited by shocamefromebay (2007-06-05 02:11:07)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Drawing the line.

trick question :'(

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shocamefromebay

Member

Registered: 2007-05-30

Posts: 103

Re: Drawing the line.

yes it is. but can u explain y???? o.O

Maelwys

Member

Registered: 2007-02-02

Posts: 161

Re: Drawing the line.

You start with zero. you must add or subtract each and every number between one thru nine. which numbers must you add or subtract to get 16 when adding or subtracting all the numbers??

Alternate answer:

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Drawing the line.

trick question :'(

It’s an excellent trick question too.

And I like Maelwys’s laterally thought-out alternative.

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: Drawing the line.

Let's make T the sum of ANY group of numbers.  Let's say the numbers are: a, b, c, d, e, f, g and h.

Now, instead of adding all the numbers in the group we're going to subtract some of them.   Let's pick b, c, and g and we'll call the new total S.   

T = a + b + c + d + e + f + g + h
S = a - b - c + d + e + f - g + h
S = T - 2b - 2c - 2g.
S = T - 2(b+c+g)

S is always going to be equal to T minus some even number.   An even number minus an even number will always yield an even number.   An odd number minus an even number will always yield an old number.   So either both T and S are even OR both T and S are odd.

shocamefromebay

Member

Registered: 2007-05-30

Posts: 103

Re: Drawing the line.

to piman's first answer, i said numbers, not digits, so urs is incorrect. and the main thing taht made this thingy impossible was taht it involved nine numbers, not 8 like in ur second response, which is what made it impossible. the nine b/c it was an odd number of numbers is what made the problem im possible. and bc urs used 8, that makes a big difference b/w our 2 problems.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Drawing the line.

to piman's first answer, i said numbers, not digits, so urs is incorrect.

I don’t see anything wrong with Pi Man’s explanation. It looks perfect to me.

Perhaps it could be reworded in the following slightly more rigorous way:

But it’s really not necessary – what Pi Man has written is good enough.

shocamefromebay

Member

Registered: 2007-05-30

Posts: 103

Re: Drawing the line.

well i guess ill be more specific next time.