Answer in 5 . 4 . 3 . 2 . 1 .....

Uncwilly · 2016-10-18, 00:12

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

petrw1 · 2016-10-18, 01:13

6 = (5 - 4) * (3 * 2 * 1)

rogue · 2016-10-18, 01:55

7 = 5 - 4 + 3 + 2 + 1

Jayder · 2016-10-18, 02:00

8 = 5 + 4 - 3 + 2 * 1

Batalov · 2016-10-18, 02:14

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)

axn · 2016-10-18, 02:59

Quote:

Originally Posted by Batalov

9 = 54 / 3 / 2 * 1

Without cheating...

9 = (5 + 4) * (3 - 2 * 1)

bsquared · 2016-10-18, 03:44

10 = (5 + 4) + (3 - (2 * 1))

Batalov · 2016-10-18, 04:19

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

VBCurtis · 2016-10-18, 04:22

17 = (5 + 4*3) * (2-1)
18 = 5 + 4*3 + 2 - 1

firejuggler · 2016-10-18, 04:36

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))

petrw1 · 2016-10-18, 05:03

22 = (5 * 4) + 3 - 2 + 1

2016-10-18, 01:13	#2
petrw1 1976 Toyota Corona years forever! "Wayne" Nov 2006 Saskatchewan, Canada 4676₁₀ Posts	I'll take 6 and pass it on... 6 = (5 - 4) * (3 * 2 * 1)

2016-10-18, 02:00	#4
Jayder Dec 2012 2×139 Posts	8 = 5 + 4 - 3 + 2 * 1 Last fiddled with by Jayder on 2016-10-18 at 02:01 Reason: Formatting

2016-10-18, 02:14	#5
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶×13 Posts	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

2016-10-18, 04:36	#10
firejuggler Apr 2010 Over the rainbow 2600₁₀ Posts	19=(54)-(3/(2+1)) 20=(54)+(3-(2+1)) or 20=(543)/(2+1) 21=(54)+(3/(2+1)) Last fiddled with by firejuggler on 2016-10-18 at 05:35*

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2016-10-18, 01:55	#3
rogue "Mark" Apr 2003 Between here and the 18CB₁₆ Posts	7 = 5 - 4 + 3 + 2 + 1

2016-10-18, 03:44	#7
bsquared "Ben" Feb 2007 3×1,171 Posts	10 = (5 + 4) + (3 - (2 * 1))

2016-10-18, 04:19	#8
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶×13 Posts	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

2016-10-18, 04:22	#9
VBCurtis "Curtis" Feb 2005 Riverside, CA 12FD₁₆ Posts	17 = (5 + 43) (2-1) 18 = 5 + 4*3 + 2 - 1

2016-10-18, 05:03	#11
petrw1 1976 Toyota Corona years forever! "Wayne" Nov 2006 Saskatchewan, Canada 2²×7×167 Posts	22 = (5 * 4) + 3 - 2 + 1