Number: .
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Let the hundreds, tens, and units digits, be H, T, and U, respectively. From clue 1, we get:
100H + 10T + U = 17(H + T + U)		
100H + 10T + U = 17H + 17T + 17U		
83H - 7T - 16U = 0 -------- eq (i)	
		
From clue 2, we get:
100H + 10T + U + 198 = 100U + 10T + H		
99H - 99U = - 198		
99(H – U) = 99(- 2)  ------- Dividing by GCF, 99		
H – U = - 2 -------- eq (ii)
 
Finally, clue 3 tells us that: 
H + U = T - 1		
H - T + U = - 1 ------ eq (iii)		

- 7H + 7T - 7U = 7 ---- Multiplying eq (iii) by - 7		
 83H - 7T - 16U = 0 --- eq (i)		
 76H - 23U = 7 -------- Adding eqs (iii) & (i) ------- eq (iv)

    H –   U = - 2 ----- eq (ii)
- 23H + 23U =  46 ----- Multiplying eq (ii) by – 23 ------- eq (v) 		
  76H – 23U =   7 ----- eq (iv)
        53H = 53 ------ Adding eqs (v) & (iv)
          H, or hundreds digit = , or 1		

1 - U = - 2 -------- Substituting 1 for H in eq (ii)		
  - U = - 2 - 1		
  - U = - 3
    U, or units digit = , or 3
		
1 – T + 3 = - 1 ------- Substituting 1 for H, and 3 for U in eq (iii)		
    4 – T = - 1
      - T = - 1 – 4
      - T = - 5
        T, or tens digit = , or 5