Classic problem: Four 4's

[fetofs]

I tried to work with the "576-x" idea. Guess what... I got a pretty tricky solution!

((4!/.4)^sq-4!^sq)/4^sq=189

14 left!

[cheesehead]

Originally Posted by Ken_g6

Concatenate (44); also before (4.4) or after (.44) a Decimal.

Ken, would the rules allow any of the following concatenations?

.(4!) = .24

(4^sq)4 = 164

4(4!) = 424

Perhaps we could require an explicit concatenation operator, such as "cat", except when only plain "4"s are concatenated in a decimal number (e.g., 44, 4.4, 444, .44, 4444, 4.444).

.cat4! = .24

4^sqcat4 = 164

4cat4! = 424



We've been using .4^sq = .16, but in that case (.4)^sq = (.)(4^sq)

[fetofs]

Originally Posted by cheesehead

Ken, would the rules allow any of the following concatenations?

.(4!) = .24

(4^sq)4 = 164

4(4!) = 424

Perhaps we could require an explicit concatenation operator, such as "cat", except when only plain "4"s are concatenated in a decimal number (e.g., 44, 4.4, 444, .44, 4444, 4.444).

.cat4! = .24

4^sqcat4 = 164

4cat4! = 424



We've been using .4^sq = .16, but in that case (.4)^sq = (.)(4^sq)

Interesting suggestion cheesehead.

If that's possible, 164-1=163
164/.8=205

[cheesehead]

To put it another (and more precise) way, what is the precedence of the concatenation operation? I think we mostly assume that it has the highest precedence, so that 4.4^sq = (4.4)^sq = 19.36, not 4.4^sq = (4.)(4^sq) = 4.16 and that 44^sq = (44)^sq = 1936, not 44^sq = (4)(4^sq) = 416.

Originally Posted by cheesehead

We've been using .4sq = .16, but in that case (.4)sq = (.)(4sq)

But for .4^sqsq, ((.4)^sq)^sq = .0256, while (.)((4^sq)^sq) = .256

[fetofs]

Originally Posted by cheesehead

To put it another (and more precise) way, what is the precedence of the concatenation operation? I think we mostly assume that it has the highest precedence, so that 4.4^sq = (4.4)^sq = 19.36, not 4.4^sq = (4.)(4^sq) = 4.16 and that 44^sq = (44)^sq = 1936, not 44^sq = (4)(4^sq) = 416.

Although the suggestion is pretty good, I wouldn't like to make things too easy...

243=(576/256)^sq*(4!+4!)

13 left!

[cheesehead]

Ah, so _that_'s how to get 3⁵.

Originally Posted by fetofs

Although the suggestion is pretty good, I wouldn't like to make things too easy...

Apparently not -- you've left 189 on the list so someone else can work on it. :-)

[Wacky]

163
177
183
187
205
213
218
223
237
283
298

[cheesehead]

Hmmm... wasn't my list correct?

[cheesehead]

A few more solutions in 3/4, 2/4 and 1/4 time:

281 = 4^sq[sup]sq[/sup]+4/.4^sq

304 = 4^sq[sup]sq[/sup]+4!+4!

316 = 4^sq[sup]sq[/sup]+4!/.4

640 = 4^sq[sup]sq[/sup]/.4

784 = (4!+4)^sq

65536 = 4^{sq[sup]sq[sup]sq}[/sup][/sup]

[Wacky]

Yes, but you cannot edit it. As I see it, continuous repetition of "the (current) list" doesn't really add anything to the discussion, but rather detracts from it in a significant manner by obscuring the more meaningful part of the discussion. That is why I have been maintaining the list in a message and periodically re-posting it so that it recains near the end of the thread.
When I do so, I've deleted the previous version of the message.

My preference would have been to keep the "scoreboard" at the very top of the thread and update it in place. The next time one of these kinds of "puzzles" (amusements that lead to a large number of responses which in some way "refine" the answer) is submitted, I request that the person posting follow the procedure that I outlined earllier in this thread. That way we can have the information presented in a usable manner and avoid cluttering the content of the thread with "status" information.

[cheesehead]

Originally Posted by Wacky

That is why I have been maintaining the list in a message and periodically re-posting it so that it recains near the end of the thread.

Okay.

When I do so, I've deleted the previous version of the message.

Oh, I hadn't noticed. Makes sense, as does your recommendation. :-)