GK 2015 Q9
9. Every asterisk in the equation 2 * 0 * 1 * 5 * 2 * 0 * 1 * 5 * 2 * 0 * 1 * 5 = 0 is to be replaced with either + or − so that the equation is correct. What is the smallest number of asterisks that can be replaced with +?
- A 1
- B 2
- C 3
- D 4
- E 5
Grey Kangaroo 2015, Question 9. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 2
The sum of the digits on the left-hand side of the equation is 24. Hence the equation formed by inserting + and − signs must be equivalent to 12 − 12 = 0. The smallest number of the given digits required to make 12 is three (2 + 5 + 5). Therefore the smallest number of asterisks that can be replaced by + is two and they would be placed in front of two of the three 5s.
Solution © UK Mathematics Trust, from the GK 2015 solutions.