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        riddles >> easy >> Adding Symbols
        
(Message started by: John_Gaughan on Feb 25th, 2004, 7:30am)
Title: Adding Symbols
Post by John_Gaughan on Feb 25th, 2004, 7:30am
1.
Add any number of the following to these equations to make them true: + - * / ( )

2 2 2 2 2 = 5
3 3 3 3 3 = 5
4 4 4 4 4 = 5
5 5 5 5 5 = 5
6 6 6 6 6 = 5
7 7 7 7 7 = 5
8 8 8 8 8 = 5
9 9 9 9 9 = 5

for example:
(2 * 2 * 2 + 2) / 2 = 5
2 + 2 + 2 - 2 / 2 = 5

I know you guys, so I will say right now the spirit of the question is to use basic arithmetic. No logs, powers, tangents, square roots, etc.

edit: you may not combine digits into new numbers, for example, "2 2" into twenty-two.

2.
Similar parameters, but different equation:
5 5 5 5 = 56
This time you can use square roots and powers, although the only numbers you can use are fives.
Title: Re: Adding Symbols
Post by Barukh on Feb 25th, 2004, 11:07am
Are we allowed to [hide]combine digits into a single number[/hide]?
Title: Re: Adding Symbols
Post by John_Gaughan on Feb 25th, 2004, 11:28am
No, like I said, just arithmetic and parenthesis.
Title: Re: Adding Symbols
Post by THUDandBLUNDER on Feb 25th, 2004, 11:36am
{[(3*3) - 3]/3} + 3 = 5

(4/4) + 4 - 4 + 4 = 5

(5*5/5) + 5 - 5 = 5

6 + 6 - 6 - (6/6) = 5

7 - (7/7) - (7/7) = 5
Title: Re: Adding Symbols
Post by Sameer on Feb 25th, 2004, 11:50am
4/4 + 4 + 4 - 4 = 5

5 + 5 - 5 + 5 - 5 = 5

6 + 6 - 6 - 6/6 = 5

7 - 7/7 - 7/7 = 5

8 - ( 8 + 8 + 8 )/8 = 5
Title: Re: Adding Symbols
Post by John_Gaughan on Feb 25th, 2004, 11:59am
Good job so far, that leaves 9... 10 and up are interesting too.
Title: Re: Adding Symbols
Post by kellys on Feb 25th, 2004, 12:39pm
[hide]( 9 * 9 + 9 ) / ( 9 + 9 )[/hide]

How about same problem if you replace all 5's by 4's.  (j/k)
Title: Re: Adding Symbols
Post by towr on Feb 25th, 2004, 12:43pm
(10 - (10 / ((10 + 10) / 10))) = 5
(15 / (((15 + 15) + 15) / 15)) = 5
(16 / (((16 + 16) + 16) / 16)) = 5
(17 / (((17 + 17) + 17) / 17)) = 5
Title: Re: Adding Symbols
Post by Quetzycoatl on Feb 25th, 2004, 1:09pm

on 02/25/04 at 12:43:05, towr wrote:
(16 / (((16 + 16) + 16) / 16)) = 5
(17 / (((17 + 17) + 17) / 17)) = 5


I don't think these come out quite right unless you are rounding down.
Title: Re: Adding Symbols
Post by Sameer on Feb 25th, 2004, 1:10pm
towr the last one i.e. the one with 17 gives 5.66666666...  ???
Title: Re: Adding Symbols
Post by towr on Feb 25th, 2004, 1:39pm
I'm using / as integer divide
we are working with integers after all :P
Title: Re: Adding Symbols
Post by Sameer on Feb 25th, 2004, 4:44pm
LOL @ integer divide

The last one

(9 + (9*9))/(9+9) = 5

Also

((11*11)-11)/(11+11) = 5
Title: Re: Adding Symbols
Post by SWF on Feb 25th, 2004, 5:24pm

on 02/25/04 at 12:39:57, kellys wrote:
How about same problem if you replace all 5's by 4's.  (j/k)

(x+x+x+x)/x = 4

Sameer, kellys already gave the solution for 9, but it was hidden.

There is no solution for 12.
Title: Re: Adding Symbols
Post by Sameer on Feb 26th, 2004, 6:28am
Hmm I didn't see any hidden answer !!! Ah well it allowed me to kill 15 minutes at work  :P

Yes you can have 5 by minimum of 6 12's.
Title: Re: Adding Symbols
Post by John_Gaughan on Feb 26th, 2004, 11:42am

on 02/26/04 at 06:28:24, Sameer wrote:
Hmm I didn't see any hidden answer !!! Ah well it allowed me to kill 15 minutes at work  :P

Yes you can have 5 by minimum of 6 12's.

I figured out that 4 and 6 12s work, but cannot get 5... so I guess you are correct on that one. I took a quick look at 13 and it does not look promising.
Title: Re: Adding Symbols
Post by SWF on Feb 27th, 2004, 4:26pm
12, 13, and 14 are impossible, as is any integer greater than 15 (with 5 of each).
Title: Re: Adding Symbols
Post by John_Gaughan on Feb 27th, 2004, 9:19pm

on 02/25/04 at 07:30:25, John_Gaughan wrote:
2.
Similar parameters, but different equation:
5 5 5 5 = 56
This time you can use square roots and powers, although the only numbers you can use are fives.

Since nobody else answered part two: it turns out that the answer to this one is 55 + 5/5 = 56. You have to put the two fives together to make fifty-five, I think. So I was wrong by saying the problem parameters were the same or "similar."
Title: Re: Adding Symbols
Post by DeMark on Feb 28th, 2004, 8:35am
8 8 8 8 8 8 8 8 = 1000    (Use just + and brackets)

1 1 1 1 1 1 = 12     (Basic arithmetics)
Title: Re: Adding Symbols
Post by John_Gaughan on Feb 28th, 2004, 12:44pm

on 02/28/04 at 08:35:15, DeMark wrote:
8 8 8 8 8 8 8 8 = 1000    (Use just + and brackets)

Is implied multiplication acceptible? Without using tricks like 8 8 = 88 this is not possible without multiplication.
Title: Re: Adding Symbols
Post by John_Gaughan on Feb 28th, 2004, 12:46pm
:: [hide]888 + 88 + 8 + 8 + 8 = 1000
11 + (1 + 1) / (1 + 1) = 12[/hide] ::
Title: Re: Adding Symbols
Post by Sameer on Mar 1st, 2004, 8:39am

on 02/27/04 at 21:19:21, John_Gaughan wrote:
Since nobody else answered part two: it turns out that the answer to this one is 55 + 5/5 = 56. You have to put the two fives together to make fifty-five, I think. So I was wrong by saying the problem parameters were the same or "similar."


*Sameer thwaps John with a big spatula for wasting his 3 hours*  >:(
Title: Re: Adding Symbols
Post by John_Gaughan on Mar 1st, 2004, 10:57am

on 03/01/04 at 08:39:32, Sameer wrote:
*Sameer thwaps John with a big spatula for wasting his 3 hours*  >:(

Hey! Thwap my coworker that gave me the puzzle! It was not me, it was the one-armed man! I swear!


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