Problem 20 · 2022 Math Kangaroo
Stretch
Algebra & Patterns
casework
Werner fills the empty squares in the calculation \(? + ? - ? = \square\) (the grey square is the result) so that the equation is correct. He always uses four of the numbers 2, 3, 4, 5, 6, and in each calculation no number may be used more than once. How many of the five numbers can Werner put in the grey square?
Show answer
Answer: E — 5
Show hints
Hint 1 of 2
You need a + b minus c = d using four distinct numbers from {2,3,4,5,6}; ask which values d can be.
Still stuck? Show hint 2 →
Hint 2 of 2
Try to hit each candidate for the grey square with some valid choice of the other three.
Show solution
Approach: construct a valid equation for each possible result
- Test each value as the grey (result) square: 3+4-5=2, 4+5-6=3, 3+6-5=4, 6+2-3=5, 5+4-3=6.
- Each uses four distinct numbers from the set, so every one of the five works.
- Hence all 5 numbers can appear in the grey square.
- So the answer is E.
Mark:
· log in to save