Label the 20 pills A through T in order of their appearance in the diagram:

The clues can be rewritten as these equations:

28=B+C+D33=B+D+E

22=F+G+H

26=F+H+I

43=H+I+J+K

21=I+J

41=J+L+M

45=M+N+O+P

39=P+Q+R+S

36=Q+S+T

22=C+G+Q

37=C+G+J+N

40=F+L+N+T

47=A+L+R+T

47=A+E+O+R

32=E+I+O

35=B+K+M

18=D+K+P

210=(sum of A through T, since they are all of 1 through 20 once each)

From 43=H+I+J+K and 21=I+J we know 22=H+K

From 28=B+C+D and 33=B+D+E we know E - C = 5

From 22=F+G+H and 26=F+H+I we know I - G = 4

From these last two results and 22=C+G+Q and 32=E+I+O we know 27=E+G+Q, 28=E+G+O, O - Q = 1

Also, from 37 = C+G+J+N and I - G = 4 and I + J = 21, we have C + N = 20

From 47=A+E+O+R, 35=B+K+M, 22=C+G+Q, 18=D+K+P, 40=F+L+N+T, 43=H+I+J+K, we know 205 = A+B+C+D+E+F+G+H+I+J+K+K+K+L+M+N+O+P+Q+R+T which yields 5 = S - 2K, or 2H+S=49.

Use these expressions to eliminate E, I, O, S, H, J, and N from the rest of the equations:

28=B+C+D0=F+G-K

24=L+M-G

24=M+P+Q-C

34=P+Q+R+2K

31=Q+2K+T

22=C+G+Q

20=F+L+T-C

47=A+L+R+T

41=A+C+Q+R

35=B+K+M

18=D+K+P

E = C + 5

I = G + 4

O = Q + 1

S = 2K + 5

H = 22 - K

J = 17 - G

N = 20 - C

Then the following expressions can be arrived at successively with substitution after each step:

34=P+Q+R+2K - (24=M+P+Q-C) + 35=B+K+M - (28=B+C+D) + 18=D+K+P - (34=P+Q+R+2K) => 1 = 2K-Q12=C+4K-F-L + 0=F+G-K - (23=C+G+2K) => 11 = L - K

0=F+G-K + 13=K+M-G => 13 = F + M

42=A+C+2K+R - (4=A+R-3K) => 38 = C + 5K

This lets everything be written in terms of K:

E = C + 5 = 43 - 5KI = G + 4 = 3K - 11

O = Q + 1 = 2K

S = 2K + 5

H = 22 - K

J = 17 - G = 32 - 3K

N = 20 - C = 5K - 18

Q = 2K - 1

T = 32 - 4K

L = 11 + K

F = 13 - M = 15 - 2K

C = 38 - 5K

G = 3K - 15

M = 2K - 2

B = 37 - 3K

D = 8K - 47

P = 65 - 9K

R = 5K - 30

A = 34 - 2K

From T = 32 - K it is known that K is no more than 7, and from A = 34 - 2K, K is at least 7. Then:

A = 20B = 16

C = 3

D = 9

E = 8

F = 1

G = 6

H = 15

I = 10

J = 11

K = 7

L = 18

M = 12

N = 17

O = 14

P = 2

Q = 13

R = 5

S = 19

T = 4

The center column contains AEHLORT, which translates to 20 8 15 18 14 5 4 by this solution, or (by index into the alphabet), THORNED.