perplexus.info :: Numbers : Two fours (or fewer?)

Two fours (or fewer?) (Posted on 2006-04-07)

There is a way to express 64 with only two fours and no symbols beyond +, -, *, /, ^, √, !, and parenthesis, although some may be used more than once. It isn't too hard. Can you find it?

It is asserted in a reliable source that 64 can also be expressed with a single 4 using 57 square root signs, nine factorials (no double or higher factorials), and 18 sets of parentheses. I can't figure it out. Can you?

Submitted by Jer

Rating: 4.0000 (2 votes)

Solution: (Hide)

sqrt(sqrt(sqrt(4^(4!))))=64 is one solution to the first part.
Demau Senae gives a solution that appears to work for the second, Dej Mar's post shows how to really do it.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Solution to the 1st Part	K Sengupta	2023-04-12 22:01:11
I have a solution to he first part	Tim	2006-04-17 01:47:45
re: Second Part, Solution	Dej Mar	2006-04-11 16:22:20
Unreliable use of reliable source	Jer	2006-04-11 12:44:22
re: Second Part	Jer	2006-04-11 12:26:36
re(2): Reliable source	Dej Mar	2006-04-10 17:59:02
re: Reliable source	Jer	2006-04-10 15:59:32
Reliable source	Jer	2006-04-10 15:50:32
Looking at the possiblities	Gamer	2006-04-10 15:16:21
Second Part:: I "Figured" it out	Dej Mar	2006-04-10 00:41:35
You're either !N or you're out	Larry	2006-04-08 16:06:15
Second Part	Demau Senae	2006-04-08 15:07:40
re: Solution to first part	Tristan	2006-04-07 22:59:59
re: better method (spoiler, first part)	Dej Mar	2006-04-07 20:36:51
better method	The riddler	2006-04-07 19:28:16
Solution to first part	Dej Mar	2006-04-07 15:27:38

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