## The 8-game

Anything goes, but keep it seemly...

### The 8-game

How many 8s do you need to make 1000? How many for 10000?

For example:
You can make 1000 with 888+88+8+8+8 using 8 8s, or 8*8*(8+8)-8-8-8 using 7...

There is no limit on operators & brackets but you cannot have any digit other than 8 and no integer/floor/ceiling/roundup functions (e.g. int[8888/8]). Also decimal points are allowed but only for something like 8.8 or 88.88, but no .8 or .88 etc for 0.8 or 0.88 (the digit 0 is not allowed)...

So far I could use 6 8's to make 1000 and 5 for 10000...
udosuk

Posts: 2698
Joined: 17 July 2005

"Multiply 8 by 8 by 8 and convert to base 8" = four
underquark

Posts: 299
Joined: 06 September 2005

If only you could find a good symbols-only expression for the "convert to base 8" operation...
udosuk

Posts: 2698
Joined: 17 July 2005

Oh, so a new rule has been introduced, has it? I'd considered using an Excel function "=DEC2OCT(8*8*8)" but realsed that it had a "2" in it.
underquark

Posts: 299
Joined: 06 September 2005

Sorry for the confusion. Here are the Rules:

1. Only digit allow is 8

2. No alphabets allowed at all, symbols only

3. No integer/floor/ceiling/roundup functions (e.g. [8.8/8]=10)

4. Everything stays in decimal system (base-10) (otherwise why don't you assume it's hexadecimal, then 1000=8*8*8*8...)

I decided to drop the ".8 not allowed" restriction to give the players more freedom...

As of now 1000 can be made with 5 8s and 10000 with 4...

Here's what I could do for 0 to 15:
Code: Select all
`num #8s0   21   22   23   34   25   36   37   38   19   310  211  312  313  414  415  4`
udosuk

Posts: 2698
Joined: 17 July 2005

underquark wrote:Oh, so a new rule has been introduced, has it? I'd considered using an Excel function "=DEC2OCT(8*8*8)" but realsed that it had a "2" in it.

You could have said "convert 8*8*8 to octal base" so only 3 8s used. But that's not the point. See above rules... In hexadecimal base I could use 2 8s only for 1000...
udosuk

Posts: 2698
Joined: 17 July 2005