Years ago when I was in college, our professor gave us a "brain teaser" and I cannot recall the answer. I hope you can help. It was something like this...

Using the numbers 0 thru 9 once each, what combination will add up to exactly 100?

I think the trick was that you needed to combine numbers, ie. 12+34 would use numbers 1,2,3,4, or 1.2+3.8 uses 1,2,3,8 and totals 5

Please send response to me at RMartin@healthcapitalinvestors.com

See

http://www.cut-the-knot.com/do_you_know/digits.html

I am a bit confused. I understood the problem to be arriving at the result of 100 using all ten numbers, including zero (0). Yet all of the solutions I have seen use only 1 through 9.

It appears to me that if the "0" is included, the solution will probably involve decimal solutions, as adding 0 to any addition of integers does not affect the result.

Possible I misunderstood the original posting.

Jack

(Trial and error)- well, you have to start from somewhere.........
use the 1 and the 0 to get 10.
then work backwards to find another 10 to multiply that 10 to get to 100.
so you need to play around with numbers 2,3,4,5,6,7,8,9

then

(6+4)* (8-5-2)*(7+3-9)
=
10*1*1
=10

Then the final answer (if I understood the question) might be:
100 = 1.0. * (6+4)(8-5-2)(7+3-9)

Similarly, say you decide to get to 100 from using 2*50.
Then you have to play around with numbers 1, 3, 6, 7, 8, 9 to get to 1.
Messing around with the numbers would then bring you to this:
use the 1 and 3 to get to 13.
then 1.3. - 6 - 7 + 9 - 8 = 1
so the answer would be..
100 = 2 * 5.0. *(1.3. - 6 - 7 + 9 - 8 )

Regards,

Ariella

I still think the problem is to come up with a total of 100 - adding numbers, but not using negative numbers - just positive numbers, although they can be decimals. There are many ways to arrive at 100 if negative numbers are used, so that is not much of a problem.

My question is: is there really a solution if only positive numbers are used? The original post implied that, but did not state it. It also implied addition as the only mathematical operation.

I have spent a few hours playing with it, using excel to do the arithmatic, but always was a shade off the desired result. It is a fun puzzle - given the restriction above. But I am not sure it has a solution.

Jack Wert

Assume there is such a sum. Then since any number is congruent to the sum of it's digits modulo 9, we have
100 ~ 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 ~ 0 mod 9
Which is a contradiction. So there is no such sum.

Thankyou

sfwc
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I forgot to mention in that post that this method also excludes using things like 1.2 + 3.8 since 0.8 ~ 8 mod 9 is just as valid.

Thankyou

sfwc
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