Problem 12 worked answer
The Ironclad’s Hidden Rest Site
Designed for Grade 2 · Uses Middle Grade 2 math · About 6–15 minutes
At a glance
- Part 1: The Rest Site is on floor 34.
Key idea
The Rest Site is the same distance from the lower Monster room and the higher Treasure room, so it is exactly halfway between them. Imagine moving both outside markers toward the Rest Site one floor at a time:
- the Monster’s floor number increases by 1;
- the Treasure’s floor number decreases by 1; and
- their sum stays unchanged because adding 1 and subtracting 1 cancel.
1. Find the forced floor
The two outside floor numbers add to 68. When both markers meet at the Rest Site, that same total has become two copies of the Rest Site’s floor:
Therefore the Rest Site is on floor 34.
Why the hidden numbers do not matter
The jump size can change the two outside rooms without moving their midpoint. A jump of 1 could give floors 33 and 35. A jump of 10 could give floors 24 and 44. Both pairs add to 68 and have 34 exactly halfway between them. Every equal-distance pair with total 68 works the same way.
Check
Using the example floors 24 and 44, the Rest Site is 10 floors above 24 and 10 floors below 44. Their sum is , and the midpoint is 34, confirming both original conditions.
Technical fit and rating
Number and operations
How the rating works →mathjewels.com/answers/problems/12/