What is the common operation?

patchy1 · 2012-07-07 14:18:25

In the 18 examples in the first two boxes below, a simple arithmetic operation on the 3-digit numbers leaves you with the 1-digit numbers. I need to figure out the required simple operation, and translate the ten numbers in the third box into the lettered solutions.

Clues:
A giveaway clue - there can be no 9's in the solution.

The arithmetic operation has two parameters - the given number and another number that is not the same for every case
- and you are looking at it.

HELP!

noelevans · 2012-07-20 08:50:45

Number the rows in the first two columns 0 through 8. Then for the ith row (i from 0 to 8) divide
the number, say n, in that row by n-i. Enter the remainder for the result, that is, n mod (n-i).
Fill out the last column using the same technique except for the last entry do 273 mod 273 to get 0.
Does this not satisfy the conditions mentioned? But this sounds too easy.

anonimnystefy · 2012-07-20 12:10:55

I don't think that's the operation, guys. That way you would get the same 1 digit answer for any 3 digit number in the i-th row.

Last edited by anonimnystefy (2012-07-20 12:11:18)

phrontister · 2012-07-20 12:27:03

Hi noelevans,

Yes, I found the same easy solution as you did but as I can't apply it to the 10th row of the third box I disregarded it, intending to find one that succeeded on all rows.

That intention then found its way into my 'to do' heap.

Last edited by phrontister (2012-07-20 12:37:31)

anonimnystefy · 2012-07-20 12:37:08

Hi phro

Did you see my reply to you?

phrontister · 2012-07-20 12:41:02

Yes I did, stefy. Still working on it, because my 'solution' is not a 'solve all' one.

Maybe that clue is incorrectly worded, because with my 'solution' it would be nice to have a 9 apply to the 10th line in the third box.

Last edited by phrontister (2012-07-20 12:53:58)

anonimnystefy · 2012-07-20 12:44:27

The non nines clues gave me the idea that some characteristic of the numbers should be looked at modulo 9, but it isn't the numbers themselves. Maybe their sum of digits or something similar.

phrontister · 2012-07-20 12:45:51

Hi stefy,

anonimnystefy wrote:

That way you would get the same 1 digit answer for any 3 digit number in the i-th row.

I don't think that the content of the first column is important...it's the finding of the 'simple operation' that is.

Last edited by phrontister (2012-07-20 15:10:13)

anonimnystefy · 2012-07-20 12:47:36

What does he operation apply to?

phrontister · 2012-07-20 12:48:59

Sorry...I wrote 'second' instead of 'first' in my previous post. Fixed it.

Last edited by phrontister (2012-07-20 12:49:25)

anonimnystefy · 2012-07-20 12:50:39

My question still holds.

phrontister · 2012-07-20 12:59:51

I don't disagree that it's a consideration, but I still think it's a possibility that the focus may be on the 'simple solution', with the first column's contents actually being irrelevant.

anonimnystefy · 2012-07-20 13:02:07

But it is clearly stated that it is an operarion on the 3-dig number and another number.

phrontister · 2012-07-20 13:06:19

Which is where my 'solution' breaks down...because of that 10th row in the third box. And I haven't progressed from there.

anonimnystefy · 2012-07-20 13:13:25

When all else fails- interpolate!

phrontister · 2012-07-20 13:16:10

Maybe this isn't really intended to be a complicated/tricky puzzle as such, but rather is more of a teaching exercise in modulo for students...hence the 'simple solution' indicator.

EDIT: I've posted a solution here. Mod(Mod(n,n-i),9) works for every row in all three boxes.

Last edited by phrontister (2016-06-16 13:17:28)

noelevans · 2012-07-20 15:19:04

I must admit the "and you are looking at it" (meaning the second number) didn't register in my mind
to begin with. So now what does that mean. Is it part of the given number, a permutation of it, or
what? Or could we be looking at it somewhere in the three columns? Somewhere within the three
columns I am seeing every digit 0 through 9. Can I then create any number I want? This opens up
a whole new ball game in my mind.

anonimnystefy · 2012-07-20 15:28:34

The problem is stunningly simple yet stunningly hard.

noelevans · 2012-07-20 15:32:06

Help Stefy!
I can't get my signature to stay on. I create it and it shows in the preview, but it doesn't show up on
my messages. Then next time I go to my profile page it has disappeared! What must I do to get it
to appear on my messages (at all much less consistently)?

Thanks!

bobbym · 2012-07-20 15:34:11

Hi noelevans;

There is a very advanced, artificial intelligence filter that is deleting it. One of the forum rules is no spam.

anonimnystefy · 2012-07-20 15:41:59

It might have to do with the Novice status you have right now.

noelevans · 2012-07-20 16:00:01

bobbym and stefy,
Thanks for your replys. Indeed I am a rank novice at navigating this site. Been teaching math for
40 some odd years, but am not very saavy at navigating on the internet. I'll try a simple one line
quote and see if that will stick. By the way, the first two times I signed up for this site the password
given to me would not work when I tried to log in. Third time was a charm. Now I can log on.
Thanks

anonimnystefy · 2012-07-20 16:02:51

Hi

You have no reason to feel as a novice. It is just a title given to newcomers After 10 posts and a particular time spent on the forum, you will recieve the title Member.

bobbym · 2012-07-20 16:06:01

Hi noelevans;

As long as you leave out the link to the page everything will be fine.

noelevans · 2012-07-20 16:14:06

Thanks again. I'm signing off and going to get some shut eye. At my age I need a good bit of it.
Blessings to you!

Math Is Fun Forum

#1 2012-07-07 14:18:25

What is the common operation?

#2 2012-07-20 08:50:45

Re: What is the common operation?

#3 2012-07-20 12:10:55

Re: What is the common operation?

#4 2012-07-20 12:27:03

Re: What is the common operation?

#5 2012-07-20 12:37:08

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#6 2012-07-20 12:41:02

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#7 2012-07-20 12:44:27

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#8 2012-07-20 12:45:51

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#9 2012-07-20 12:47:36

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#12 2012-07-20 12:59:51

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