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five fives

five fives

Posers and Puzzles

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I know four fours have been done here (not sure about 5 5s though)
You have to form the numbers from 0-whatever (in ascending order) using simple arithmetic operations. These being:

addition +
subtraction -
multiplication *
division /
factorial !
concatenation (eg: 55 or.55 etc...)
decimals . (ie .5)
recurring decimals (no overbar (or underline) so will let .5 denote .555555.... = 5/9)
square roots sqrt() (debatable because of implied 1/2 but then factorial has implied 2,3,4 in it yet no-one says anything about that)
exponentiation ^

Also since the first 30 or so are trivial should we start a bit later?

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5!/5 + 5 + 5/5 = 30
5*5 + 5 + 5/5 = 31
Hmmm...... = 32
5.5 * 5 + 5.5 = 33
5!/5 + sqrt(5)*sqrt(5) + 5 = 34
5(5 + 5/5) + 5 = 35

LaTeX would make this forum much nicer, though it's not that easy to implement probably.

5 edits
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Originally posted by Kristaps
5!/5 + 5 + 5/5 = 30
5*5 + 5 + 5/5 = 31
Hmmm...... = 32
5.5 * 5 + 5.5 = 33
5!/5 + sqrt(5)*sqrt(5) + 5 = 34
5(5 + 5/5) + 5 = 35

LaTeX would make this forum much nicer, though it's not that easy to implement probably.
Yeah I agree with you about the LaTeX...the boldface for recuring .5... looks crappy!
((sqrt(5*5) + 5)/5)^5 = 32🙂

36 = (5!/(5+5))*(sqrt(5/.5)
37 = (((5+5)/5)^5)+5
38 = (5!/(5*.5))-5-5
39 = (5!/(5*.5)) -5/.5
40 = ((5*5)/.5) -5-5

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About LaTeX - Thread 119064

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41 = 5*(5+5)-5/.5

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LaTeX with greasemonkey for those using Firefox.
Thread 108499

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Originally posted by Palynka
LaTeX with greasemonkey for those using Firefox.
Thread 108499
Thanks for that.

Now back to the topic

42 = meaning of li.... = ...

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42 = ((5*5)/.5) - sqrt(5/.5)

4 edits
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43 = 5!/sqrt(5/.5) + sqrt(5/.5)
44 = 5*5/.5 - 5/5
45 = 5*5/.5 - 5 + 5
46 = 5*5/.5 + 5/5
47 = (5*5 + .5 + .5)/.5
48 = 5!/5*(5+5)/5
49 = 5*(5+5)-5/5
50 = 5*(5+5)-5+5
51 = 5*(5+5)+5/5

6 edits
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52 = (5*5 +(5/5))/.5
53 = 55 - (5+5)/5
54 = 55 -5^(5-5)
55 = 55 -5*(5-5)
56 = 55 +5^(5-5)
57 = 55+ (5+5)/5
58 = 5!/(5*.5) +5+5
59 = 55 + 5 - (5/5)
60 = 55 + 5*(5/5)
61 = 55 +5 + (5/5)

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I think I'll skip.

.5 is 0.5, so it uses a zero we don't get.

sqrt uses a 2

Factorial is a function, not an operation.

0.555.... uses at least three 5's as typed here. Creating an abbreviation feels like cheating.

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62:

5.5 x 5.5 x ( 5/5 + 5/5) + 0.5 + 0.5 + 0.5

thats probably too many fives

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With too many 5s, its easy:
62 = 55 + 5 + 5/5 + 5/5
...still thinking...

4 edits
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62 = 5*5*5*.5 - .5
63 = 5*5*5*.5 + .5
64 = (5! + (5 - .5)/.5)*.5
65 = (5! + (5 + .5)/.5)*.5

1 edit
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