This monthly post is a reminder to set aside a few minutes for yourself to take part in the joy of problem solving.
Give it a try, and feel free to leave a hint, but no spoilers! This week, share an observation or problem solving strategy that might help someone else get started. We’ll welcome solutions next week!
This monthly post is a reminder to set aside a few minutes for yourself to take part in the joy of problem solving.
Give it a try, and feel free to leave a hint – but no spoilers! Share an observation or problem solving strategy that might help someone else get started. We’ll welcome solutions next week!
Solution:
A Smarter Approach to Guess & Check...
You're trying to fill the circles so each line adds up to 20. While you could just guess, let's first look at the structure to make more informed guesses!
Count the Total: If each of the three lines adds up to 20, that's a total of 3 × 20 = 60.
Sum of All Numbers: The numbers 1 through 9 add up to 45. (That's 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45).
The "Extra" Corners: Notice that the three corner numbers are counted twice (once for each line they're on). The difference between our total (60) and the sum of all numbers (45) tells us the sum of those "extra" corner numbers: 60 − 45 = 15.
Pick Your Corners: Start by choosing any three numbers that add up to 15 for the corners.
Fill in the Rest: Now using Guess & Check is a bit simpler. Fill in the remaining circles, ensuring each line sums to 20.
(Looking for More? Answer: The other sums could be: 17, 19, 21 and 23.)
Problem Solving Tip: Before jumping in, it's always helpful to take a moment to understand the problem and notice what information you have.
Stay tuned for a new Problem of the Month next week!
How did you solve it?
We’d love to hear the journey you went on to solve Eight Numbers, Four Equations. What did you notice? What strategies did you try? What road blocks did you encounter? What emotions were you feeling while trying this?
Tell your story in words, a picture, or a video.
Ready for more?
Keeping the same layout (see image above) and still using the numbers 1-8, find a new arrangement of operations using +, –, ×, or ÷. Repeat operations are allowed. How many different arrangements can you discover where the boxes can be filled to create four true equations?