Math HELP!

[EmperorJeramyu]

"A government issues only two kinds of coins: one of 7 units, and one 11 units. Thus, certain prices cannot be paid exactly, for example: 15 units. What is the highest price that CANNOT be paid with any combination of the two coins? HINT: You may use as many of the coins as needed."

A friend and I have been laboring at this for a while, but we're stupid, so we need help. Perhaps a resident genious (Read: DSOK), could help us out, and provide some reasoning behind the answer. Thanks.

[Iteroth]

Haha I hate math. I had to do it in summer school once.

PS: This is what part of the alphabet would look like if you got rid of Q and R.

[Flibbo]

i dont get that at all

if you can use as many of the coins as you want then there is no answer surely, it just keep going up

[OverlordBill]

It's like the game Bizz Buzz. You need to find the last number you actually say before everything just turns to saying Bizz Buzz every time. Try writing a program for it.

[Excell]

There is no maximum number that you can achieve because there is no such thing as a maximum number. Infinity doesn't exist. Therefore the answer is that there is no maximum number that it cannot achieve.

[EmperorJeramyu]

We got 70. Every number after that can be made using a combination of 7s and 11s.

[DSOK]

"A government issues only two kinds of coins: one of 7 units, and one 11 units. Thus, certain prices cannot be paid exactly, for example: 15 units. What is the highest price that CANNOT be paid with any combination of the two coins? HINT: You may use as many of the coins as needed."

A friend and I have been laboring at this for a while, but we're stupid, so we need help. Perhaps a resident genious (Read: DSOK), could help us out, and provide some reasoning behind the answer. Thanks.

I'm flattered.
In fact, this is my area of greatest expertise; I have a doctorate in mathematics.

First, let me provide an elementary proof that there is a largest such number. Note that you can obtain both 21 (3 x 7) and 22 (2 x 11). This is the first pair of adjacent integers you get. Adding these two together in all possible ways, you can get 42, 43, and 44. Adding those together gives all numbers from 84 through 88, and adding those pairwise gives every integer from 168 to 176. Since this last list of consecutive integers is more than seven long, every form 7n + k for k =0, 1, 2, 3, 4, 5, and 6 is represented. Every larger number can therefore be represented as one of these numbers, plus a multiple of 7.

Notice that 11 = 7 + 4, so any of the larger numbers 18, 25, 32, etc., with the form 7n + 4 can be written as a multiple of 7 plus 11. Similarly, 22 = 3 x 7 + 1, 33 = 4 x 7 + 5, 44 = 6 x 7 + 2, 55 = 7 x 7 + 6, and 66 = 9 x 7 + 3. At this point, we have all the forms 7n + k, so any larger number than 66 can be written as 7n + 11m. The largest number that can't be written in this form is 66 - 7 = 8 x 7 + 3 = 59. This is because 7n + 3 was the last form to be added to our list, and 59 is the largest number with this form that is less than 66.

[Excell]

Haha, I wish you had listened to my bullshit answer. I had no idea what the real answer was but that woulda been funny as shit if you had gone in with "none".

[Sage Of The Wise]

I'm told I'm gifted in math, but that explanation just hurt my head. Had to read it about 5 times to get it, well sort of get it.

[DSOK]

Haha, I wish you had listened to my bullshit answer. I had no idea what the real answer was but that woulda been funny as shit if you had gone in with "none".

Oh, yeah, that would have been an incredible riot.

Anyway, I started writing my response before yours was posted.

[Glenn47]

Lol, 10th grade geometry, and I STILL don't know that?

Nice going dude. Jeneus's liek us have to stick together exponinshally.

[EmperorJeramyu]

...Whoah... DSOK. Awesome. The man with the crazy mad math skills.

[DSOK]

Lol, 10th grade geometry, and I STILL don't know that?

Nice going dude. Jeneus's liek us have to stick together exponinshally.

It's good to know that will be able to count on your support in the coming times of crisis.

[Excell]

Yes, it would have. Especially because there was no chance of Jeramyu doing anything back.

[Telephalsion]

well if I was more fluent in english math terms i'd have understood that...

oh well I sort of uderstood that. the smallest item you can purchase is something worth 4, pay 11 get 7 back.

EDIT: after looking throung it again I understad it, y=kx+m