July 31st, 2017, 11:23 AM  #1 
Senior Member Joined: Apr 2014 From: zagreb, croatia Posts: 234 Thanks: 33 Math Focus: philosophy/found of math, metamath, logic, set/category/order/number theory, algebra, topology  Obtain 64 with two 4s
This has been done before, but still it could be interesting. You can do anything, only out of all the numbers, you can use only 4, and only two times. Last edited by skipjack; July 31st, 2017 at 11:29 AM. 
July 31st, 2017, 11:31 AM  #2 
Senior Member Joined: Apr 2014 From: zagreb, croatia Posts: 234 Thanks: 33 Math Focus: philosophy/found of math, metamath, logic, set/category/order/number theory, algebra, topology 
I have no patience. $\displaystyle \sqrt{\sqrt{\sqrt{4^{4!}}}}$ 
July 31st, 2017, 11:43 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,250 Thanks: 1439 
Or $\sqrt{\sqrt{√4}}^{4!}$ and the like.

July 31st, 2017, 12:42 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,086 Thanks: 723 
4!!^sqrt(4) = 64

July 31st, 2017, 12:46 PM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,086 Thanks: 723 
Using only one 4: ounces in 4 pounds = 64 
July 31st, 2017, 01:27 PM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,678 Thanks: 1339  
July 31st, 2017, 04:07 PM  #7 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 607 Thanks: 83 Math Focus: Electrical Engineering Applications 
4 << 4 (4 represented in binary, bit shifted left 4 times). Edit: Originally had 'binary 4' which I don't like. Last edited by jks; July 31st, 2017 at 04:11 PM. 
August 25th, 2017, 08:04 PM  #8 
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 371 Thanks: 68 
4×(4 squared)

August 26th, 2017, 10:00 AM  #9 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361 
Using three fours: 4 * 4 * 4 = 64 
August 26th, 2017, 10:12 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,086 Thanks: 723 
Hoempa, go stand in the corner for 64 minutes...


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