IMC 2007 Q18
18. One of the digits 1 to 9 is put in each unshaded square so that no digit is repeated and the totals of the entries in the rows and columns are as shown.
What number goes in the starred square?
- A 1
- B 3
- C 5
- D 7
- E 9
| Total | ||||
|---|---|---|---|---|
| 12 | ||||
| 7 | ||||
| * | 13 | |||
| Total | 4 | 16 | 12 |
Intermediate Mathematical Challenge 2007, Question 18. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 5
From the second row we see that \(c\), \(d\), \(e\) are 1, 2, 4 in some order; and from the third column we see that \(e > 2\). Hence \(e = 4\) and we may now deduce that \(g = 8\) and so \(f = 5\).
(Although their values are not required, it is now also possible to deduce that \(c = 1\), \(a = 3\), \(b = 9\), \(d = 2\).)
| Total | ||||
|---|---|---|---|---|
| \(a\) | \(b\) | 12 | ||
| \(c\) | \(d\) | \(e\) | 7 | |
| \(f\) | \(g\) | 13 | ||
| Total | 4 | 16 | 12 |
Solution © UK Mathematics Trust, from the IMC 2007 solutions.