How can I get these numbers only using 1 through 5?

Question

16, 17, 18, 19, 23, 24, 26, 27, 28, 29, 31.

First off, you cannot repeat the same number each time ( meaning you can only use "1" once when finding 16) Also no exponents. Only the numbers 1 - 5

Answer 1

3*5+1=16
3*5+2=17
4*5-2=18
3*5+4=19
4*5+3=23
5*4+3+1=24
5*(2+3)+1=26
5*(2+4)-3=27
4*(2+5)=28
4*(2+5)+1=29
5*(2+4)+1=31

Answer 2

I assume that you want to use 1, 2, 3, 4, and 5 together with addition, subtraction, mutiplication, and division to obtain the numbers you listed.

You didn't say whether you have to use all of the numbers 1 to 5 or if just using some of them is okay, so I decided to err on the side of caution and used all of them in each case. (If this isn't required, it certainly doesn't hurt anything.)

16 = 3 * 5 + 4 - 2 - 1
17 = 1 * 2 * 5 + 3 + 4
18 = 3 * 5 + 4 - 2 + 1
19 = 1 * 4 * 5 + 2 - 3
23 = 1 * 3 * 5 + 2 * 4
24 = 3 * 5 + 2 * 4 + 1
26 = 4 * 5 + 1 + 2 + 3
27 = 2 * 3 * 5 + 1 - 4
28 = 2 * 3 * 4 + 5 - 1
29 = 1 * 2 * 3 * 4 + 5
31 = 5 * 3 * 4 / 2 + 1

Answer 3

16 = (3 X 5) + 1
17 = (3 X 5) +2
18 = (4 X 5) -2
19 = (4 X 5) -1
23 = (4 X 5) +3
24 = (4 X 5) +3 +1
26 = (4 X 5) + (3 X 2)
27 = (4 X 5) + (3 X 2) + 1
28 = (4 X 3 X 2) + (5 - 1)
29 = (5 X 3 X 2 ) - 1
31 = (5 X 3 X 2 ) + 1

Answer 4

16 = 3 * 5 + 1
17 = 3 * 5 + 2
18 = 3 * 5 + 1 + 2
19 = 3 * 5 + 4
23 = 4 * 5 + 3
24 = 4 * 5 + 3 + 1
26 = 4 * 5 + 3 + 2 + 1
27 = (4 + 1) * 5 + 2
28 = (4 + 1) * 5 + 3
29 = (4 + 2) * 5 - 1
30 = (4 + 2) * 5 + 1

Answer 5

16 = 5x3 + 1
17 = 5x3 + 2
18 = (5+1)x 3
19 = (4+2)*3 + 1
23 = 5x4 +3
24 = 4 x (5 + 1)
26 = 4x(5+1) + 2
27 = 4x(5+1) + 3
28 = 4x(5+2)
29 = 4x(5+2) +1
31 = 4x(5+2) + 3

Answer 6

.,,3x5+1=16,,3x5+2=17,,3x5+2+1=18,, 4x5-1=19,,
4x5+2+1=23,,4x5+3+1=24, ,4x5+3+2=25,,
4x5+1+2+3=26,,(4+1)x5+2=27,, (4+1)x5+3=28
(4+2)x5-1=29,,(4+2)x5+1=31,,
the end.

Answer 7

16=5x3+1
17=5x3+2
18=5x4-2
19=5x4-1
23=5x4+3
24=2x3x4
26=4x5+3x2
27=(4+5)x3
28=2x3x4+(5-1)
29=2x3x4=5
31=(2+4)x5+1