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Old 2016-10-18, 00:12   #1
Uncwilly
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Default Answer in 5 . 4 . 3 . 2 . 1 .....

The following is borrowed from here.
Quote:
Take the digits 5, 4, 3, 2 and 1, in that order. Using those digits and the four arithmetic signs — plus, minus, times and divided by — you can get 1 with the sequence 5 - 4 + 3 - 2 - 1. You can get 2 with the sequence (5 - 4 + 3 - 2) x 1.

The question is ... how many numbers from 1 to 40 can you get using the digits 5, 4, 3, 2, and 1 in that order along with the four arithmetic signs?

You can group digits with parentheses, as in the example. There are no tricks to this, though. It's a straightforward puzzle. How many numbers from 1 to 40 can you get — and, specifically, what number or numbers can you not get?
Let's try to keep it with out powers or bases. Also, let's try to get variants for each number
Color any additions that you make.
Code:
 1 = 5 - 4 + 3 - 2 - 1
 2 = (5 - 4 + 3 - 2) x 1
 3 = (5 + 4) - (3 x 2 x 1)
 4 = -5 + 4 + (3 x 2) - 1
 5 = -5 + (4 x 3) - 2 x 1
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Old 2016-10-18, 01:13   #2
petrw1
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Default I'll take 6 and pass it on...

6 = (5 - 4) * (3 * 2 * 1)
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Old 2016-10-18, 01:55   #3
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7 = 5 - 4 + 3 + 2 + 1
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Old 2016-10-18, 02:00   #4
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8 = 5 + 4 - 3 + 2 * 1

Last fiddled with by Jayder on 2016-10-18 at 02:01 Reason: Formatting
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Old 2016-10-18, 02:14   #5
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9 = 54 / 3 / 2 * 1

Because 5+4+3+2+1 = 15, each odd number up to 15 is easy: just change one or more pluses into a minus. It is much more interesting to use a minimal number of signs (less than four; then obviously you will have some more than 1-digit numbers)

Last fiddled with by Batalov on 2016-10-18 at 04:12
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Old 2016-10-18, 02:59   #6
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Quote:
Originally Posted by Batalov View Post
9 = 54 / 3 / 2 * 1
Without cheating...

9 = (5 + 4) * (3 - 2 * 1)
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Old 2016-10-18, 03:44   #7
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10 = (5 + 4) + (3 - (2 * 1))
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Old 2016-10-18, 04:19   #8
Batalov
 
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11 = 5 + 4 + 3 - 2 + 1
12 = 5 + 4 + 3 * (2 - 1)
13 = 5 + 4 + 3 + 2 - 1
14 = 5 + 4 + 3 + 2 * 1
15 = 5 + 4 + 3 + 2 + 1
16 = 5 + 4 + 3 * 2 + 1
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Old 2016-10-18, 04:22   #9
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17 = (5 + 4*3) * (2-1)
18 = 5 + 4*3 + 2 - 1
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Old 2016-10-18, 04:36   #10
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19=(5*4)-(3/(2+1))
20=(5*4)+(3-(2+1)) or 20=(5*4*3)/(2+1)
21=(5*4)+(3/(2+1))

Last fiddled with by firejuggler on 2016-10-18 at 05:35
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Old 2016-10-18, 05:03   #11
petrw1
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22 = (5 * 4) + 3 - 2 + 1
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