(A)
+----+----+----+----+----+
| 19 |    | 22 |  6 |    | 
+----+----+----+----+----+
| 9  |    | 23 | 20 | 7  |  Total = 80
+----+----+----+----+----+
| 20 |    | 16 |    |    | 
+----+----+----+----+----+
|    |    | 9  |    | 27 | 
+----+----+----+----+----+
|    | 14 | 10 | 32 | 13 | 
+----+----+----+----+----+

(B)
+----+----+----+----+----+
|    | 13 | 21 | 3  |    | 
+----+----+----+----+----+
| 14 |    | 20 |    |  4 |  Total = 75
+----+----+----+----+----+
| 20 | 23 | 15 |  7 | 10 | 
+----+----+----+----+----+
|    | 12 | 10 |    | 31 | 
+----+----+----+----+----+
|    |  8 |  9 | 36 |    | 
+----+----+----+----+----+

Each row, column and five-figure diagonal line totals 80 in diagram A and totals 75 in diagram B.

Three different positive integers must be used to fill up the blank cells, as many times as necessary, to achieve this for each of (A) and (B).

Find the missing numbers for each of (A) and (B).

*** Three distinct numbers in (A) and (B) may differ.

(A)
+----+----+----+----+----+
| 19 | 12 | 22 |  6 | 21 | 
+----+----+----+----+----+
| 9  | 21 | 23 | 20 | 7  |  Total = 80
+----+----+----+----+----+
| 20 | 21 | 16 | 11 | 12 |  with 11, 12, 21
+----+----+----+----+----+
| 21 | 12 | 9  | 11 | 27 | 
+----+----+----+----+----+
| 11 | 14 | 10 | 32 | 13 | 
+----+----+----+----+----+
(B)
+----+----+----+----+----+
| 19 | 13 | 21 | 3  | 19 | 
+----+----+----+----+----+
| 14 | 19 | 20 | 18 |  4 |  Total = 75
+----+----+----+----+----+
| 20 | 23 | 15 |  7 | 10 |  with 11, 18, 19
+----+----+----+----+----+
| 11 | 12 | 10 | 11 | 31 | 
+----+----+----+----+----+
| 11 |  8 |  9 | 36 | 11 | 
+----+----+----+----+----+

Posted by Charlie on 2014-06-19 15:26:15