In Give Question,
A + B = 8 ---- (i)
A + C =13 -----(ii)
B + D = 8 ----(iii)
C - D = 6 ----(iv)
Therefore equation (i) and (iii) are equal
A + B = B + D
=> A = D
Therefore, equation (iv) can be C - A = 6 ----- (v)
Now solving equation (ii) and (v), We Get C = 9.5 and A = 3.5
Put this value of A in equation in (i) B = 4.5 and value of C in equation (iv) we get D = 3.5

A = 3.5
B = 4.5
C = 9.5
D = 3.5

Starting at the top and working down, add 5 to the numerical value of any even numbered letter, and add 7 to the numerical value of any odd numbered letter to give the letters in the space below.

Starting with the letters in segments of the top left circle, add 3 to the numerical values of the letters, and write the results in the top right circle, with the relative positions of the letters moving 1/4 turn clockwise. Repeat this pattern, adding 4 to the values of the letters for the lower right hand circle, and adding 5 for the letters in the lower left hand circle, putting the results in the segments 1/4 turn clockwise each time.

Starting at the top and working in diagonal lines from top right to bottom left, letters alternately increase in value by 9, then decrease by 3.

In each diagram, start with the letter in the top left and move clockwise around the others. Letters advance through the alphabet in steps given by the numerical value of the central letter.

The sum of the numerical values of the letters around each star is always 55.

Split the diagram horizontally into 3 rows, each 2 circles high. Start with the top left circle in each row, and move one space to the right, alternating down and up. Letters advance through the alphabet 5 letters at a time for the upper double row, 6 letters at a time for the central row, and 7 letters at a time for the bottom row.

In each circle, the digit is equal to the number of straight lines used to write the two letters in the same circle.

Start at the top left and move to the right, then down one row and to the left etc in a snakes and ladders pattern. Letters advance through the alphabet 9 letters at a time.

Start with the J in the top left and move anti-clockwise around the shape in an hourglass shape. Letters advance through the alphabet in steps of 11 letters at a time.

Starting with the bottom row and moving up, one row at a time, the sum of the numerical values of the letters starts at 26 for the bottom row, then 24, 22 and 20 as you move up.

Using the letters in the top right circle as a source, add 4 to the numerical values of each letter to give the letters in corresponding segments of the middle circle, and subtract 5 from the values to give the letters in corresponding segments of the bottom circle.

Starting with the bottom left letter and moving in a clockwise spiral towards the centre, letters advance through the alphabet in steps of 4, 5, 6 etc.

Starting with the bottom right hand corner, and moving in a clockwise spiral towards the centre, letters advance through the alphabet, skipping 4 letters at a time.

Starting at the top left, and moving to the right, then down one row and to the left etc. in a snakes and ladders pattern, letters advance through the alphabet by 5 steps, then back 2, repeating this pattern for the rest of the diagram.

Missing Character, Y - 2 = W.

Starting in the top left corner and moving clockwise in a spiral towards the centre, letters follow the alphabetic sequence, skipping 5 letters at a time, written in alternate squares of the diagram.

Taking pairs of letters in the inner and outer segments of each eighth of the diagram, the numerical values always add up to 20. So, A + ? = 20 1 + ? = 20 ? = 19 = S.

The sum of the numerical values of pairs of letters, opposite each other in the diagram, is always 20 (the numerical value of the central letter).

Working in columns, add together the numerical values of the first and second letters, and put the letter with the reverse alphabetical value of this sum in the bottom space.

Starting with the G, move clockwise around the circle, in steps of 3 letters, then 4, 5, 6 and 7. So, N + 5 = 14 + 5 = 19 = S.

As you move down, letters are written in alphabetical order, skipping any letters written with curved lines. Next Letter = I.

First Row A ----(+3)---> D ----(+3)---> G.

Second Row D ----(+5)---> I ----(+5)---> N.

Third Row I ----(+7)---> P ----(+7)---> W.

Starting with the top left outer segment and moving clockwise, letters advance through the alphabet in steps of 4, then 5, 6, 7 etc. The letters in the inner segments follow the same pattern, but move anti-clockwise.

Starting at the top left and working anti-clockwise towards the centre in a spiral, letters advance through the alphabet in steps of 8 at a time. So, Missing Character, Y + 8 = G.

Taking pairs of letters in adjacent segments, their numerical values always add up to 10. So, D + ? = 10 4 + ? = 10 ? = 6 = F
Missing Character = F.

Start with the top left circle, and move in horizontal lines from left to right, top to bottom, across all 4 shapes. Letters are written in alphabetical order, in steps of 5 letters at a time.

Converting all letters to their numerical values, the middle section of each row of the diagram contains a list of letters which are common multiples of a number, given by the value of the letter in the right hand box. One letter in each row does not follow this sequence, and is put in the left hand box.

Each box is filled with the letter of the alphabet you find one place after the vowels. So, Last vowel is U and letter proceeding U is V. Missing Character = V.

Start at the top left segment of the left hand circle and move clockwise, then to the middle circle and move anti-clock- wise, and finally to the right hand circle and move clockwise again. Letters are written in alphabetical order, in steps of 4 letters at a time. So, Missing Character, D + 4 = H.

Starting with the upper left hand box of the left hand diagram, and moving to the right, letters follow the alphabetical order, 5 letters at a time. A second sequence starts from the middle of this row and goes down, with letters following the alphabetic order, 6 letters at a time. Repeat this pattern for the other diagrams, using steps of 6 and 7 letters, 7 and 8 letters, and 8 and 9 letters.