7UP number theory

[Upchurch]

What the heck is the algorythm at work behind this one?

 

[Ladewig]

What the heck is the algorithm at work behind this one?

Hint: the difference between two numbers that have the same digits in a different order will always be a multiple of nine.

 

[tkingdoll]

A full solution is here: http://ubersite.com/m/72587

 

[Upchurch]

very nice. thank you

 

[Nucular]

A full solution is here: http://ubersite.com/m/72587

I scrolled down and read the comments first. I confess to a little flash of superior irritation at the thoughtful comment "WTF IM NOT READING ALL THAT". Scrolling back up to the solution, I rethought and decided I'd found a soul-mate.

Neat idea and realisation though, however incomprehensible to me.

 

[Kotatsu]

What the heck is the algorythm at work behind this one?

It's easy: he tells you to write it down on a note, and then he peeks at the note. Even though he asks you not to show the note to him! He's a sneaky person, he.

 

[Nucular]

Ah, having had a bit of a play around, I see you can do it yourself without the special program, and it works for numbers of any length of digits.

All you have to do, after you've made someone go through the mill and circle a number, is to add up the remaining numbers as they read them out to you. You then work out what the nearest multiple of 9 is, and the difference between that and the total you've arrived at is the number they've circled.

 

[blutoski]

Hint: the difference between two numbers that have the same digits in a different order will always be a multiple of nine.

... in base 10. (I've had to do this proof soooo many times)

 

[aofl]

Ah, having had a bit of a play around, I see you can do it yourself without the special program, and it works for numbers of any length of digits.

All you have to do, after you've made someone go through the mill and circle a number, is to add up the remaining numbers as they read them out to you. You then work out what the nearest multiple of 9 is, and the difference between that and the total you've arrived at is the number they've circled.

IMHO, it's a lot easier to just cast out nines when they read the numbers to you. The easiest way to do this is to add the numbers as they read them to you, and if the total has two digits, then add those two digits. At the end, you'll be left with the number you subtract from nine to get the circled answer.

e.g. 2, 6, 4, 8

2+6 = 8
8 + 4 = 12 => 1 + 2 = 3
3 + 8 = 11 => 1 + 1 = 2

A

 

[T'ai Chi]

I put up a page on this neat number trick a bit ago

http://www.statisticool.com/digitalroot.htm