Problem 9 · 2019 Math Kangaroo
Medium
Algebra & Patterns
arithmetic-sequenceoff-by-one
Linda fixes 3 photos on a pin board next to each other. She uses 8 pins to do so (see picture). Peter wants to fix 7 photos in the same way. How many pins does he need for that?
Show answer
Answer: B — 16
Show hints
Hint 1 of 2
Look at the picture: the first photo needs 4 pins (its 4 corners), but each new photo touches the one before it.
Still stuck? Show hint 2 →
Hint 2 of 2
Because neighbours share their pins, every photo after the first adds the same small number of pins.
Show solution
Approach: see the repeating add-on for each photo
- The top row of pins has one more pin than the number of photos, and so does the bottom row.
- For 3 photos that is 4 pins on top and 4 pins on the bottom, which makes 8 pins — this matches the picture.
- For 7 photos it is 8 pins on top and 8 pins on the bottom.
- Counting both rows gives 8 + 8 = 16 (B).
Mark:
· log in to save