Help me crack the codes!

[hampus_dh]

Hello, so as i went to work today my friend told me and another guy a math trick his friend had gotten from the university.

He never told my friend how to do it so we stopped working and started to figure out how he did it (info below)

Anyway we finally cracked one code, and by code i mean that you don´t have to count everytime but instead you find a pattern so that when that number pops up you can instantly say what the other number will be (again info below).

Anyway, here´s how it goes.

You can choose how many numbers you want but they have to be 0-9,

So for example it could be 2+4+5+6+7+7 but to make it easy let´s start with this for now:

5+9 = 14

You then take 5+9 and remove the + and subtract that with 14 in this case.

So, 59 - 14 = 45

Now you have the number 45 right. You give me one of these numbers, let´s say number 4.

I don´t know any of the other calculations above or the other number apart from the number 4.
And it´s my job to figure out the other number, in this case 5.

So basically if anyone here would do a calculation as above, any numbers you like except that you have to end up with 2 numbers and give me just one of them i could tell you the other number right away.

There is calculation i have to do to figure out that other number but since my college spent all day trying to figure out how to do it we saw a pattern in how to quickly tell the other number if there are only two of them, one of which we know.

If anyone don´t understand my crappy english then please just do the calculation above and tell me one of the numbers and i´ll tell you what number you have hidden.

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the point i´m trying to make is that i would like help to find the other "codes" in which you don´t have to do lengthy calculations to figure out the missing number but instead can use this pattern to quickly figure out which number is hidden.

 

[Techy]

To help out, here's some more examples that shows an apparent pattern:

Two-Step
1) 6 + 9 = 15
69 - 15 = 54

2) 7 + 9 = 16
79 - 16 = 63

3) 8 + 9 = 17
89 - 17 = 72

4) 9+9=18
99-18=81

5) 10+9=19
109-19=90

Apparent Pattern = +9, as first number raised by 1

Three-Step:

1) 1+1+1=3
111-3=108

2) 2+2+2=6
222-6=216

3) 3+3+3=9
333-9=324

Apparent Pattern = +108, as per number raised by 1

Four-step:

1) 1+2+3+4=10
1234-10=1224

2) 2+3+4+5=14
2345-14=2331

3) 3+4+5+6=18
3456-18=3438

Apparent Pattern = +1107, as per number raised by 1 from 1, 2, 3, 4

Five-step:
1) 2+1+2+1+2=8
21212-8=21204

2) 2+2+2+2+2=10
22222-10=22212

3) 2+3+2+3+2=12
23232-12=23220

Apparent pattern = +1008, as each 2nd number raised by 1

Ten-step:

1)1+1+1+1+1+1+1+1+1+2=11
1111111111-11=1,111,111,100

2)1+1+1+1+1+1+1+1+1+4=13
1111111111-13=1,111,111,098

Apparent pattern = -2, as last number raised by 2

I did choose random numbers, so other people's investigations may be more limited and/or more reasonable.

According to what I did though, the formula is:

a+b=c
(a+b)-c=final

a+b+c=d
(a+b+c)-d=final

a+b+c+d=e
(a+b+c+d)-e=final

And so on. The numbers you choose for a, b, c, and so on will always form a pattern, so that's one rule. The relationship between each one however is unknown. But what I did see is that the higher the numbers for a, b, c, etc., the pattern gets very large. And as the ten-step one, using very small numbers resulted in a loss. But this can be easily contradicted if someone tests it out and got something different. For me, I did enough for now

Sorry if this wasn't what you want. I think I went a bit overboard But it could probably be used to figure out the hidden number.

EDIT: Also, I'm not sure what will happen if you use numbers by tens, hundreds, etc., probably the pattern will be boosted even higher, like to millions maybe.

 

[hampus_dh]

Holy smokes

You did so much you managed to get me lost

the code i know is the one you figured out pretty damn quick, for the two numbers i.e.

9-0
8-1
7-2
6-3
5-4

Give me a minute and i´ll read through that one more time

Edit: Ok i confess, i do understand but not at that level i want to

Assume i say 5 and 4. Figure out the third number.

Would you be able to figure out instantly without any calculations what that number is?

 

[Daniel]

Add all of the digits in the final answer [/Chris Tarrant] add up to 9.
3-digit number?
He gives you 3 and 4?
Last number is 2.

To help out, here's some more examples that shows an apparent pattern:

Two-Step
1) 6 + 9 = 15
69 - 15 = 54

Both numbers add up to nine

1+2+3+4=10
1234-10=1224

2+1+2+1+2=8
21212-8=21204

1+1+1+1+1+1+1+1+1+2=11
1111111112-11=1 111 111 101

1+1+1+1+1+1+1+1+1+4=13
1111111114-13=1 111 111 101

5 + 4 = 9
1 + 2 + 2 + 4 = 9
2 + 1 + 2 + 0 + 4 = 9
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 0 + 1 = 9
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 0 + 1 = 9

Assume i say 5 and 4. Figure out the third number.

Would you be able to figure out instantly without any calculations what that number is?

Zero (5 + 4 + 0 = 9)

I'll try my own for clarity:

3 + 7 + 5 + 6 = 21
3756 - 21 = 3735*
3 + 7 + 3 + 5 = 18
1 + 8 = 9

*If that number doesn't add up to nine, then you'll have 'go deeper' and add up the digits again

The most thinking I had to do was sorting the Color and Bold tags around all the quotes.
Hope I helped

 

[hampus_dh]

Ok i think i got it down now Thanks!

You can´t believe how long we sat wondering how the hell he managed to know the other number if we only gave him one

9 is what everything should add up to whether that is just one or several.

 

[DG_Silva]

Basically, you'd be looking for a multiple of 108 that features 5, 4 and another number.

EDIT: @daniel, he said 5 and 4, not 3 and 4. So technically speaking the correct answer would be 0.

 

[Daniel]

Oh, I know that. That was an example. 'Scuse the ninja edits as well

 

[hampus_dh]

i think i come across a problem.

How fo you know if the number the person has hidden is a 0 or 9?

 

[Daniel]

Can you give an example? I can't think of when you would need to choose between 0 and 9. If the numbers given add up to 9 exactly, then most likely the last will be 0.

 

[hampus_dh]

Can you give an example? I can't think of when you would need to choose between 0 and 9. If the numbers given add up to 9 exactly, then most likely the last will be 0.

My other friend has the note but i will give example as soon as i can.
But so if it adds up to 9 then it will for sure be a 0?

Just by looking at it?

What if you everything is added up to 9 but you hide a 9?

 

[DG_Silva]

Let's say you get a 7 and 2, which add up to 9. Basically, you've got to guess. However, as there is no multiple of 108 that features a 7, 2 and 0, the educated guess would be 9. Thus 2+7+9=18 -> 1+8=9. If the total you have exceeds 9, then you have to total 18 (next multiple of 9).

But in answer to your question, you've got to find a multiple of 108, and the numbers you have will be your guide.

 

[hampus_dh]

Let's say you get a 7 and 2, which add up to 9. Basically, you've got to guess. However, as there is no multiple of 108 that features a 7, 2 and 0, the educated guess would be 9. Thus 2+7+9=18 -> 1+8=9. If the total you have exceeds 9, then you have to total 18 (next multiple of 9).

But in answer to your question, you've got to find a multiple of 108, and the numbers you have will be your guide.

Ok thanks, this and Daniels posts have bern very helpful