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Topic: Adding Symbols (Read 592 times) |
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John_Gaughan
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Adding Symbols
« on: Feb 25th, 2004, 7:30am » |
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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.
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| « Last Edit: Feb 25th, 2004, 11:30am by John_Gaughan » |
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Barukh
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Re: Adding Symbols
« Reply #1 on: Feb 25th, 2004, 11:07am » |
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Are we allowed to combine digits into a single number?
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John_Gaughan
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Re: Adding Symbols
« Reply #2 on: Feb 25th, 2004, 11:28am » |
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No, like I said, just arithmetic and parenthesis.
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ThudnBlunder
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Re: Adding Symbols
« Reply #3 on: Feb 25th, 2004, 11:36am » |
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{[(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
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| « Last Edit: Feb 25th, 2004, 11:55am by ThudnBlunder » |
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Sameer
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Re: Adding Symbols
« Reply #4 on: Feb 25th, 2004, 11:50am » |
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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
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| « Last Edit: Feb 25th, 2004, 11:50am by Sameer » |
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John_Gaughan
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Re: Adding Symbols
« Reply #5 on: Feb 25th, 2004, 11:59am » |
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Good job so far, that leaves 9... 10 and up are interesting too.
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kellys
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Re: Adding Symbols
« Reply #6 on: Feb 25th, 2004, 12:39pm » |
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( 9 * 9 + 9 ) / ( 9 + 9 )
How about same problem if you replace all 5's by 4's. (j/k)
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towr
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Re: Adding Symbols
« Reply #7 on: Feb 25th, 2004, 12:43pm » |
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(10 - (10 / ((10 + 10) / 10))) = 5
(15 / (((15 + 15) + 15) / 15)) = 5
(16 / (((16 + 16) + 16) / 16)) = 5
(17 / (((17 + 17) + 17) / 17)) = 5
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Quetzycoatl
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Re: Adding Symbols
« Reply #8 on: Feb 25th, 2004, 1:09pm » |
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on Feb 25th, 2004, 12:43pm, towr wrote:
(16 / (((16 + 16) + 16) / 16)) = 5
(17 / (((17 + 17) + 17) / 17)) = 5 |
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I don't think these come out quite right unless you are rounding down.
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| « Last Edit: Feb 25th, 2004, 1:31pm by Quetzycoatl » |
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Sameer
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Re: Adding Symbols
« Reply #9 on: Feb 25th, 2004, 1:10pm » |
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towr the last one i.e. the one with 17 gives 5.66666666... 
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"Obvious" is the most dangerous word in mathematics.
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Proof is an idol before which the mathematician tortures himself.
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towr
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Re: Adding Symbols
« Reply #10 on: Feb 25th, 2004, 1:39pm » |
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I'm using / as integer divide
we are working with integers after all 
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Sameer
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Re: Adding Symbols
« Reply #11 on: Feb 25th, 2004, 4:44pm » |
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LOL @ integer divide
The last one
(9 + (9*9))/(9+9) = 5
Also
((11*11)-11)/(11+11) = 5
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SWF
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Re: Adding Symbols
« Reply #12 on: Feb 25th, 2004, 5:24pm » |
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on Feb 25th, 2004, 12:39pm, kellys wrote:| How about same problem if you replace all 5's by 4's. (j/k) |
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(x+x+x+x)/x = 4
Sameer, kellys already gave the solution for 9, but it was hidden.
There is no solution for 12.
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Sameer
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Re: Adding Symbols
« Reply #13 on: Feb 26th, 2004, 6:28am » |
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Hmm I didn't see any hidden answer !!! Ah well it allowed me to kill 15 minutes at work
Yes you can have 5 by minimum of 6 12's.
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"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
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John_Gaughan
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Re: Adding Symbols
« Reply #14 on: Feb 26th, 2004, 11:42am » |
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on Feb 26th, 2004, 6:28am, Sameer wrote:Hmm I didn't see any hidden answer !!! Ah well it allowed me to kill 15 minutes at work
Yes you can have 5 by minimum of 6 12's. |
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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.
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SWF
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Re: Adding Symbols
« Reply #15 on: Feb 27th, 2004, 4:26pm » |
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12, 13, and 14 are impossible, as is any integer greater than 15 (with 5 of each).
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John_Gaughan
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Re: Adding Symbols
« Reply #16 on: Feb 27th, 2004, 9:19pm » |
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on Feb 25th, 2004, 7:30am, 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. |
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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."
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DeMark
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Re: Adding Symbols
« Reply #17 on: Feb 28th, 2004, 8:35am » |
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8 8 8 8 8 8 8 8 = 1000 (Use just + and brackets)
1 1 1 1 1 1 = 12 (Basic arithmetics)
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John_Gaughan
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Re: Adding Symbols
« Reply #18 on: Feb 28th, 2004, 12:44pm » |
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on Feb 28th, 2004, 8:35am, DeMark wrote:| 8 8 8 8 8 8 8 8 = 1000 (Use just + and brackets) |
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Is implied multiplication acceptible? Without using tricks like 8 8 = 88 this is not possible without multiplication.
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John_Gaughan
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Re: Adding Symbols
« Reply #19 on: Feb 28th, 2004, 12:46pm » |
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:: 888 + 88 + 8 + 8 + 8 = 1000
11 + (1 + 1) / (1 + 1) = 12 ::
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Sameer
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Re: Adding Symbols
« Reply #20 on: Mar 1st, 2004, 8:39am » |
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on Feb 27th, 2004, 9:19pm, 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." |
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*Sameer thwaps John with a big spatula for wasting his 3 hours* 
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"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
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John_Gaughan
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Re: Adding Symbols
« Reply #21 on: Mar 1st, 2004, 10:57am » |
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on Mar 1st, 2004, 8:39am, Sameer wrote:| *Sameer thwaps John with a big spatula for wasting his 3 hours* |
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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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