Question

Shown below are three types of interlocking rods. There are in total 12 rods: 6 of type A (8 cm), 2 of type B (5 cm), and 4 of type C (4 cm). What is the maximum straight length obtainable by connecting the rods appropriately?

Hint:

When chaining interlocking elements of different “genders,” push unavoidable overlaps onto the fewest joints (ideally the shortest modules) and place neutral pieces at the extremities to keep both ends lossless.

Answer 1

Step 1: Add the usable body lengths.
If no joint caused any extra “loss”, the total from bodies would be
\(6\times 8 + 2\times 5 + 4\times 4 = 48 + 10 + 16 = 74\) cm.
Step 2: Use rod ends to minimise joint loss.
Place the two B rods at the two ends of the chain (so their end interlocks don’t force any extra insertion loss at the extremities).
Insert the four C rods as the only places where an additional 1 cm of overlap is unavoidable (each C connection “eats” 1 cm of effective length).
All remaining joints can be arranged as simple plug–socket connections that do not reduce the effective body sum further.
Step 3: Compute the maximum.
Loss \(= 4 \times 1\text{ cm} = 4\text{ cm}\). Hence, maximum obtainable length
\[ 74\text{ cm} - 4\text{ cm} = \boxed{70\text{ cm}}. \]