Four 4s

Kai Laddiman · Post by **Kai Laddiman** » Sat Jun 13, 2009 10:05 pm

Yes, it's that puzzle that everyone has already done, it's Four 4s!

You have to use all four 4s to make every number from 1 to 100. Pretty simple.

You can use most functions; if they are dubious, ask about them.

Banned functions:

Integer brackets []
Trigonononononometric thingies sin cos tan etc.
Powers
Stuff like that.

First person to get 1 wins a signed VFSMB.

Daniel O'Dowd · Post by **Daniel O'Dowd** » Sat Jun 13, 2009 10:13 pm

Sorry; what is the significance of 'integer' brackets [] as opposed to ()?

Kai Laddiman · Post by **Kai Laddiman** » Sat Jun 13, 2009 10:19 pm

Daniel O'Dowd wrote:Sorry; what is the significance of 'integer' brackets [] as opposed to ()?

Integer brackets ignore decimals, for example [sqrt(sqrt(4))] would be the integer of sqrt 2, ie. 1.

Matt Morrison · Post by **Matt Morrison** » Sat Jun 13, 2009 10:22 pm

Kai Laddiman wrote:First person to get 1 wins a signed VFSMB.

1 = (4/4)*(4/4)

Steve Durney · Post by **Steve Durney** » Sat Jun 13, 2009 10:57 pm

Matt Morrison wrote:
Kai Laddiman wrote:First person to get 1 wins a signed VFSMB.
1 = (4/4)*(4/4)

2= (4/4)+(4/4)

Innis Carson · Post by **Innis Carson** » Sat Jun 13, 2009 10:59 pm

Steve Durney wrote:
Matt Morrison wrote:
Kai Laddiman wrote:First person to get 1 wins a signed VFSMB.
1 = (4/4)*(4/4)
2= (4/4)+(4/4)

3= (4*4-4)/4

Charlie Reams · Post by **Charlie Reams** » Sat Jun 13, 2009 11:20 pm

4 = 4

Howard Somerset · Post by **Howard Somerset** » Sat Jun 13, 2009 11:23 pm

Charlie Reams wrote:4 = 4

The rules say you need to use all four fours.

So (4-4)x4+4 = 4

Michael Wallace · Post by **Michael Wallace** » Sat Jun 13, 2009 11:24 pm

Howard Somerset wrote:
Charlie Reams wrote:4 = 4
The rules say you need to use all four fours.

So (4-4)x4+4 = 4

You've used five 4s...

Charlie Reams · Post by **Charlie Reams** » Sat Jun 13, 2009 11:25 pm

Michael Wallace wrote:
Howard Somerset wrote:
Charlie Reams wrote:4 = 4
The rules say you need to use all four fours.

So (4-4)x4+4 = 4
You've used five 4s...

You've used a 5.

Howard Somerset · Post by **Howard Somerset** » Sat Jun 13, 2009 11:26 pm

Michael Wallace wrote:
Howard Somerset wrote:
Charlie Reams wrote:4 = 4
The rules say you need to use all four fours.

So (4-4)x4+4 = 4
You've used five 4s...

No. I've used only four 4s. The fifth is the result.

Michael Wallace · Post by **Michael Wallace** » Sat Jun 13, 2009 11:27 pm

Howard Somerset wrote:No. I've used only four 4s. The fifth is the result.

It would seem my 'humour' is wasted here

Howard Somerset · Post by **Howard Somerset** » Sat Jun 13, 2009 11:28 pm

Michael Wallace wrote:
Howard Somerset wrote:No. I've used only four 4s. The fifth is the result.
It would seem my 'humour' is wasted here

We'd have difficulty when we get to 44.

Howard Somerset · Post by **Howard Somerset** » Sat Jun 13, 2009 11:30 pm

Looking ahead a little:

Is sqrt allowed?
Is factorial allowed?

Matt Morrison · Post by **Matt Morrison** » Sat Jun 13, 2009 11:38 pm

May the fours be with you.

Howard Somerset · Post by **Howard Somerset** » Sat Jun 13, 2009 11:40 pm

Am I allowed to go for the next one too?

If so, (4x4+4)/4 = 5

Ben Hunter · Post by **Ben Hunter** » Sat Jun 13, 2009 11:47 pm

((4 + 4) / 4) + 4 = 6

Howard Somerset · Post by **Howard Somerset** » Sat Jun 13, 2009 11:51 pm

4 + 4 - 4/4 = 7

Matt Morrison · Post by **Matt Morrison** » Sat Jun 13, 2009 11:54 pm

I'm not afraid to admit that 14 is stumping me.

A clear definition of which functions we can and can't use might help?

Howard Somerset · Post by **Howard Somerset** » Sat Jun 13, 2009 11:56 pm

Matt Morrison wrote:I'm not afraid to admit that 14 is stumping me.

A clear definition of which functions we can and can't use might help?

If it's allowed, then 4 x 4 - 4 + sqrt(4) = 14

Matt Morrison · Post by **Matt Morrison** » Sat Jun 13, 2009 11:58 pm

Howard Somerset wrote:
Matt Morrison wrote:I'm not afraid to admit that 14 is stumping me.

A clear definition of which functions we can and can't use might help?
If it's allowed, then 4 x 4 - 4 + sqrt(4) = 14

Cool. I'd avoided square roots, but they're officially in now. Thumbs up for factorials too.

Howard Somerset · Post by **Howard Somerset** » Sun Jun 14, 2009 12:01 am

I'm sure that when I did this at school in 1953 we used sqrt and factorial. And I think it was somewhere in the 30s where we got stuck.

After allowing [], which Kai has outlawed, pretty well anything becomes possible.

We also used concatenation, which Kai needs to rule upon, e.g. 44 + 44 = 88

Marc Meakin · Post by **Marc Meakin** » Sun Jun 14, 2009 12:04 am

Howard Somerset wrote:
Michael Wallace wrote:
Howard Somerset wrote:No. I've used only four 4s. The fifth is the result.
It would seem my 'humour' is wasted here
We'd have difficulty when we get to 44.

44 + 4-4 = 44

David Roe · Post by **David Roe** » Sun Jun 14, 2009 12:31 am

(4 + 4) * 4 / 4 = 8

Howard Somerset · Post by **Howard Somerset** » Sun Jun 14, 2009 12:38 am

4 + 4 + 4/4 = 9

Innis Carson · Post by **Innis Carson** » Sun Jun 14, 2009 12:48 am

(4-(4/4))! + 4 = 10

Daniel O'Dowd · Post by **Daniel O'Dowd** » Sun Jun 14, 2009 12:58 am

4+((4!+4)/4)=11

Howard Somerset · Post by **Howard Somerset** » Sun Jun 14, 2009 1:00 am

4 x 4 - sqrt(4 x 4) = 12

Daniel O'Dowd · Post by **Daniel O'Dowd** » Sun Jun 14, 2009 1:08 am

4!−(44/4)=13

Jon O'Neill · Post by **Jon O'Neill** » Sun Jun 14, 2009 1:09 am

(4!4+4!+4)/4=13

Howard Somerset · Post by **Howard Somerset** » Sun Jun 14, 2009 1:13 am

4!/4 + 4 + 4 = 14

Howard Somerset · Post by **Howard Somerset** » Sun Jun 14, 2009 1:14 am

Jon O'Neill wrote:(4!4+4!+4)/4=13

Second 4 should be removed. Nice one.

Innis Carson · Post by **Innis Carson** » Sun Jun 14, 2009 1:14 am

(4*4) - (4/4) = 15

Daniel O'Dowd · Post by **Daniel O'Dowd** » Sun Jun 14, 2009 1:17 am

4x4x4/4=16

Howard Somerset · Post by **Howard Somerset** » Sun Jun 14, 2009 1:19 am

4x4+4/4=17

Matt Morrison · Post by **Matt Morrison** » Sun Jun 14, 2009 1:39 am

Daniel O'Dowd wrote:4!−(44/4)=13

(4!+4!+4)/4 without concatenation

Liam Tiernan · Post by **Liam Tiernan** » Sun Jun 14, 2009 1:40 am

4*4 +(4 /sqrt4 )=18 4!-4-(4/4)=19

Howard Somerset · Post by **Howard Somerset** » Sun Jun 14, 2009 1:44 am

4 x (4 + 4/4) = 20

Howard Somerset · Post by **Howard Somerset** » Sun Jun 14, 2009 1:47 am

Matt Morrison wrote:(4!+4!+4)/4 without concatenation

I think that's what Jono was trying to say. He put an extra 4 in by mistake.

Liam Tiernan · Post by **Liam Tiernan** » Sun Jun 14, 2009 1:48 am

4!-4-4+4=20 4!-4 +(4/4)=21 4*4+4+sqrt4=22

Daniel O'Dowd · Post by **Daniel O'Dowd** » Sun Jun 14, 2009 1:53 am

You missed 18:

4!-Sq4-Sq4-Sq4=18

Michael Wallace · Post by **Michael Wallace** » Sun Jun 14, 2009 1:54 am

Daniel O'Dowd wrote:You missed 18:

4!-Sq4-Sq4-Sq4=18

Liam Tiernan wrote:4*4 +(4 /sqrt4 )=18

Liam Tiernan · Post by **Liam Tiernan** » Sun Jun 14, 2009 1:54 am

((4!*4)-4)/4=23

Howard Somerset · Post by **Howard Somerset** » Sun Jun 14, 2009 1:56 am

4! - 4/sqrt(4x4) = 23

4! x 4/sqrt(4x4) = 24

4! + 4/sqrt(4x4) = 25

Liam Tiernan · Post by **Liam Tiernan** » Sun Jun 14, 2009 1:57 am

(44+4)/sqrt4=24

Liam Tiernan · Post by **Liam Tiernan** » Sun Jun 14, 2009 1:59 am

((44/4)*sqrt4)+4=26

Liam Tiernan · Post by **Liam Tiernan** » Sun Jun 14, 2009 2:05 am

4!+4-(4/4)=27

Liam Tiernan · Post by **Liam Tiernan** » Sun Jun 14, 2009 2:09 am

4!+4+4-4=28 4!+4+(4/4)=29 4!+4+(4/sqrt4)=30

Kai Laddiman · Post by **Kai Laddiman** » Sun Jun 14, 2009 7:58 am

Howard Somerset wrote:Looking ahead a little:

Is sqrt allowed?
Is factorial allowed?

Yup and yup.

Kai Laddiman · Post by **Kai Laddiman** » Sun Jun 14, 2009 8:02 am

OK then, the following functions are allowed:

sqrt
factorial ! (sorry Charlie) and any variants of it
concatenation (although it is possible to get them all without it

)

And, yeh, I think that's it. And by factorial variations, well, Wikipedia!

Kai Laddiman · Post by **Kai Laddiman** » Sun Jun 14, 2009 8:04 am

Er, I'm having trouble keeping up with all of these solutions (I sleep), but I think we've got all of the ones up to 30, no?

Howard Somerset · Post by **Howard Somerset** » Sun Jun 14, 2009 8:37 am

Kai Laddiman wrote:
Howard Somerset wrote:Looking ahead a little:

Is sqrt allowed?
Is factorial allowed?
Yup and yup.

Glad to hear that. I think this puzzle is made possible because sqrt(4) is an integer.
But I was concerned when you outlawed powers, because sqrt is simply a power of 0.5. Glad you've allowed this exception.

Liam Tiernan wrote:4!+4+4-4=28 4!+4+(4/4)=29 4!+4+(4/sqrt4)=30

Good to see you didn't carry on too much further after I'd gone to bed. I was expecting to see many more done by this morning.

Howard Somerset · Post by **Howard Somerset** » Sun Jun 14, 2009 8:43 am

Another couple of questions:

Can we have decimal points? e.g. 4/.4 = 10
Can we have recurring decimals? e.g.

Code: Select all

   .
4/.4   = 9

If so, then

Code: Select all

        .
4! + 4/.4 - sqrt(4) = 31

Jon O'Neill · Post by **Jon O'Neill** » Sun Jun 14, 2009 8:53 am

Howard Somerset wrote:
Matt Morrison wrote:(4!+4!+4)/4 without concatenation
I think that's what Jono was trying to say. He put an extra 4 in by mistake.

Thanks Howard. Drunk.

Kai Laddiman · Post by **Kai Laddiman** » Sun Jun 14, 2009 8:57 am

Howard Somerset wrote:Another couple of questions:

Can we have decimal points? e.g. 4/.4 = 10
Can we have recurring decimals? e.g.
Code: Select all
   .
4/.4   = 9
If so, then
Code: Select all
        .
4! + 4/.4 - sqrt(4) = 31

Er, if you absolutely have to, then use decimal points. Although it's possible without them...

Howard Somerset · Post by **Howard Somerset** » Sun Jun 14, 2009 8:57 am

Jon O'Neill wrote:
Howard Somerset wrote:
Matt Morrison wrote:(4!+4!+4)/4 without concatenation
I think that's what Jono was trying to say. He put an extra 4 in by mistake.
Thanks Howard. Drunk.

YW. Guessed so.

David Williams · Post by **David Williams** » Sun Jun 14, 2009 10:15 am

We were given this at school to occupy us for half an hour while our teacher did his pools. I got stuck at (I think) 33. Years later, lying on a beach, I suddenly thought "Decimals! And recurring decimals!!" (I have good holidays.)

After that I had another bash and kept a dog-eared piece of paper with all I could get up to about 500. I'm proud to say that when I discovered the internet I'd got every single one that's possible without using gamma functions and natural logarithms.

Liam Tiernan · Post by **Liam Tiernan** » Sun Jun 14, 2009 10:34 am

Next one's easy (4*4)+(4*4)=32

Matt Morrison · Post by **Matt Morrison** » Sun Jun 14, 2009 11:09 am

Apologies Jono, didn't notice yours was for 13 too, not trying to steal your thunder!
But yeah if Kai says it can be done without concatenation and decimals, let's do it without. I'm still stuck on 31.

Liam Tiernan · Post by **Liam Tiernan** » Sun Jun 14, 2009 11:17 am

Next one..........not so easy.