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**Darby****Member**- Registered: 2011-10-14
- Posts: 7

I lay awake at night staring at the (digital) clock, and try to make equations as each minute passes by...I have all the 11 and 12 o`clock ones figured out, and most of the 10`s. Can you help with 10:26, 10:27, 10:28 and a few others I am sure you will come across as difficult. You can use any functions including roots and factorials (with the exception of the inequality sign!), however all the digits MUST be in order (as seen on the clock), and (except for square roots with their implied `2`)any root function MUST be warranted by the digit being already present.

Examples : 12:30 1+2=3+0 11:57 1+1+5=7 10:41 1+0=(sqrt)4-1 12:38 1x2=(3root)8

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

hi Darby

i sometimes like to do that game w/ old car registrations

which contain only numbers in it,but i allow myself to change the order,and restrict myself to the four basic operations!

10=2+8?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi Darby;

10:26

(1+0+2)! = 6

10:28

10 = 2+8

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Darby****Member**- Registered: 2011-10-14
- Posts: 7

I tried to quote bobbym in this reply, but evidently I don't know how to do that. Thank you for your quick answers.....do you sometimes want to just bang your head quietly on a desk? Some very rudimentary equations there.....I am a little sheepish. And to anonimnystefy, where I live the license plates have three letters and three numbers so I have an easier time making words from the letters....three numbers is often not a lot to work with mathematically...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Do you allow integer functions?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Darby****Member**- Registered: 2011-10-14
- Posts: 7

I am not immediately familiar with those....can you give some examples?

I'm a C+ Algebra 11 student (although Algebra 11 was decades ago....)

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi;

That is the floor function there is also a ceiling function.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Darby****Member**- Registered: 2011-10-14
- Posts: 7

bobbym wrote:

Hi;

That is the floor function there is also a ceiling function.

I see what you mean. That would be stretching things just a bit, but in the absence of any other exact solutions I suppose it would be OK. As long as everything isn't *quickly* solved by this application (sort of like my "cheater" way on the 11 o'clock equations where almost every one of them can be written as 1 being equal to a power of one.....)

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**Darby****Member**- Registered: 2011-10-14
- Posts: 7

These are the only ones I have left to get:

10:27, 10:38, 10:47, 10:57, 10:58, 10:59

If you can get those, you are better than I am (like that hasn't been proved already....)

Thanks, and have fun.

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**reconsideryouranswer****Member**- Registered: 2011-05-11
- Posts: 172

Darby wrote:

1 = (0 X 2 X 7)!

1 = (0/2 X 7)!

1 = [0 X (2 + 7)]!

1 = [0 X (2 - 7)]!

1 = [0 X 2^7]!

1 = [0/(2^7)]!

1 = (0^27)!

1 = [0^ (2 X 7)]!

1 = [0^(2^7)]!

1 = [(0^2)^7]!

1 = [0^2 X 7]!

1 = [0^(2/7)]!

1 = [(0/2)/7]!

1 = [(0 X 2)/7]!

1 = (0/2/7)!

1 = (0/2 X 7)!

1 = (0/27)!

1 = [0/(2 X 7)]!

1 = [(0 X 2)^7]!

1 = [(0/2)^7]!

1 = [0/(2^7)]!

1 = [0/(2 + 7)]!

Signature line:

I wish a had a more interesting signature line.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi Darby;

I am sorry but I have been unable to find anything for those that does not use something more complicated then what you have been using.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Darby****Member**- Registered: 2011-10-14
- Posts: 7

reconsideryouranswer wrote:

Darby wrote:1 = (0 X 2 X 7)!

1 = (0/2 X 7)!

1 = [0 X (2 + 7)]!

1 = [0 X (2 - 7)]!

1 = [0 X 2^7]!

1 = [0/(2^7)]!

1 = (0^27)!

1 = [0^ (2 X 7)]!

1 = [0^(2^7)]!

1 = [(0^2)^7]!

1 = [0^2 X 7]!

1 = [0^(2/7)]!

1 = [(0/2)/7]!

1 = [(0 X 2)/7]!

1 = (0/2/7)!

1 = (0/2 X 7)!

1 = (0/27)!

1 = [0/(2 X 7)]!

1 = [(0 X 2)^7]!

1 = [(0/2)^7]!

1 = [0/(2^7)]!

1 = [0/(2 + 7)]!

I like this, because it actually solves all the rest as well. I went over all my equations to see if I had used zero as an exponent (another defined term) and I hadn't - and these fit the criteria so closely they work. Plus....I lack the mathematical depth to continue searching for some elusive root of some elusive factorial....

Thanks!!

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**reconsideryouranswer****Member**- Registered: 2011-05-11
- Posts: 172

bobbym wrote:

Hi Darby;

I am sorry but I have been unable to find anything for those

that does not use something more complicated then what

you have been using.

10:38

1 = [0(3 + 8)]!

- - - - - - - - - -- -

10:47

1 = [0(4 + 7)]!

- - - - - - - - - - -

10:57

1 = [0(5 + 7)]!

- - - - - - - - - - -

10:58

1 = [0(5 + 8)]!

- - - - - - - - - -

10:59

1 = [0(5 + 9)]!

__________________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

*Last edited by reconsideryouranswer (2011-10-15 13:22:03)*

Signature line:

I wish a had a more interesting signature line.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi;

When I posted post #11. I did not see your solution else I would not have posted.

reconsideryouranswer wrote:

What is holding you up about these, bobbym!?

Darby wrote:

I like this, because it actually solves all the rest as well.

Darby is satisfied, what is there left for me to do?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Darby****Member**- Registered: 2011-10-14
- Posts: 7

Ok, I know this is now an OLD thread and someone is likely to chide me on that point and refer me to a more appropriate method of posting this query which, though, is essentially a follow-up to the above. My initial numbers were limited to those four digit numbers appearing on a digital clock - since then I decided that seeing as there were only 10,000 four digit combinations I would attempt to solve every single one of them. It has taken me months, and I am left with only four unsolved combinations. They are:

2667 7662

2710 8757

I have employed all the familiar operators, plus, minus, divide, mutiply, roots, exponents, factorials and have for about the last twenty or so gone to the use of DOUBLE factorials (like 7675 being 7! / 6! = 7!! / 5!!), and in a couple of instances DECIMAL notation (like 5657 being .5 = 6 / (5+7)).

If someone could set those last four to bed, I could move on with my life. Thank you!!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi Darby;

I am not getting them either!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**cool_jessica****Member**- Registered: 2012-06-26
- Posts: 15

I just love playing with numbers . Basically series, its is so amazing that every number series has a solution to it. Just think carefully and it will be solved.

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