🕷️ The spider that slipped down the wall

A closer look at one question · SMC 2024, Question 29 (bank id C4)

A spider started climbing a garden wall from the bottom. After climbing 1/3 of the wall, it rained, and the spider slipped DOWN 30 cm and waited there. Once the rain stopped, it climbed the remaining 5/6 of the wall's height to reach the top. What was the TOTAL height the spider climbed, before and after the rain?

1 Follow the spider's journey, one stage at a time

🕷️ Start at the bottom (0)

↑ climbs 1/3 of the wall

Reaches 1/3 of the way up — then it rains

↓ slips DOWN 30 cm

Stuck lower down, waiting out the rain

↑ climbs the remaining 5/6 of the wall

🏁 Reaches the TOP

2 The three moves add up to exactly ONE wall

1/3 up, then 30 cm down, then 5/6 up — and it ends exactly at the top. In sixths, 1/3 + 5/6 = 2/6 + 5/6 = 7/6 of the wall. That is more than one whole wall — by exactly 1/6 — and that extra 1/6 is precisely the 30 cm it slipped back down.

1/6 of wall

= 30 cm

So the whole wall is 6 × 30 = 180 cm tall.

3 Add up what was actually CLIMBED (not the slip)

Before rain

1/3 of 180 = 60 cm

After rain

5/6 of 180 = 150 cm

60 + 150 = 210 cm climbed in total.

210 cm

The trap: answering 180 — that is the height of the WALL. The question asks how far the spider CLIMBED, which is more, because it had to re-climb the 30 cm it slipped.