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-   -   Four Fours (https://www.mersenneforum.org/showthread.php?t=7051)

Andi47 2007-03-30 16:18

167 with less gammas:

167 = Γ(4) * (4! + 4) - Γ(√4)

173 and 185 with only one gamma:

173 = (Γ(4)! - 4! - 4) / 4
185 = (Γ(4)! + 4) / 4 + 4

[QUOTE=DJones;102023]207 = (4! * gamma(4) - gamma(4)) / √.4~
[/QUOTE]

Or, without gamma:

207 = (4 * 4! - 4) / .4~

P.S.: Is it allowed to use the n-th root?

219 = [sup].4[/sup]√(4 / .4~) - 4!

Andi47 2007-03-30 16:34

242 = 4 * 4! / .4 + √4
243 = (√4 / √.4~) ^ (√4 / .4)
244 = 4[sup]4[/sup] - 4! / √4
245 = (4 * 4! + √4) / .4

cheesehead 2007-03-30 16:45

246 = 4 ^ 4 - (4 / .4)
247 = 4 ^ 4 - (4 / .4~)
248 = 4 ^ 4 - 4 - 4

Andi47 2007-03-30 17:03

249 = 4[sup]4[/sup] - Γ(4) - Γ(√4)
250 = 4[sup]4[/sup] - 4 - √4
251 = 4[sup]4[/sup] - √4 / .4
252 = 4[sup]4[/sup] - √4 - √4

petrw1 2007-03-30 20:43

[QUOTE=Andi47;102515]
P.S.: Is it allowed to use the n-th root?

219 = [sup].4[/sup]√(4 / .4~) - 4![/QUOTE]

I like it, I think it's very inventive ... anyone object?

cheesehead 2007-03-31 03:09

253 = 4[sup]4[/sup] - √(4 / .4~)
254 = 4[sup]4[/sup] - (4 / √4)
255 = 4[sup]4[/sup] - (4 / 4)
256 = [sup]4[/sup]√((4[sup]4[/sup])[sup]4[/sup])
or
256 = 4 * 4 * 4 * 4

I think [sup]4[/sup]√ is just fine, since it doesn't imply a number other than 4.

Andi47 2007-03-31 05:58

257 = 4[sup]4[/sup] + 4 / 4
258 = 4[sup]4[/sup] + 4 - √4
259 = 4[sup]4[/sup] + √4 / √.4~
260 = 4[sup]4[/sup] + √4 + √4

cheesehead 2007-03-31 06:23

261 = 4[sup]4[/sup] + √4 / .4
262 = 4[sup]4[/sup] + 4! / 4
263 = 44 * Γ(4) - Γ(√4)
264 = 44 * 4! / 4

Andi47 2007-03-31 06:51

265 = 4[sup]4[/sup] + 4 / .4~
266 = 4[sup]4[/sup] + 4 / .4
267 = [sup].4[/sup]√(4 / .4~) + 4!
268 = 4[sup]4[/sup] + 4! / √4

cheesehead 2007-04-02 05:58

269 = ((√4/.4)! - .4~) / .4~
270 = (4 + 4/4)! / .4~
271 = ((√4/.4)! + .4~) / .4~
272 = 4[sup]4[/sup] + 4*4

Andi47 2007-04-02 08:07

273 = gamma(4)! * .4 - gamma(4) / .4
274 = (√4 / .4)! / .4~ + 4
275 = (44 / .4) / .4
276 = 4[sup]4[/sup] + 4! - 4


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