Question

Four students (K, L, M, N) participate in four competitions (Quiz, Debate, Chess, Coding), one event each.
1. K does not do Quiz or Chess.
2. L does Coding.
3. N does not do Debate.
4. M does not do the same event type as K.
How many valid assignments are possible?

Hint:

When each person must take a unique role, assign the most constrained individuals first. This reduces the search space dramatically.

Answer 1

Correct Answer: 2

We have four events: Quiz (Qz), Debate (Db), Chess (Ch), Coding (Cd). Each student must take exactly one unique event.
Step 1: Assign L. 
L does Coding. \[ L = Cd \] Remaining events: Qz, Db, Ch. 
Remaining students: K, M, N.
Step 2: Apply K’s restriction. 
K does not do Quiz or Chess: \[ K \neq Qz,\ K \neq Ch \] Thus the only remaining event K can take is: \[ K = Db \] Step 3: Apply N’s restriction. 
N does not do Debate: \[ N \neq Db \] But Db is already taken by K, so N can only take from \[Qz, Ch\]. 
Step 4: Apply M’s restriction. 
M does not do the same event as K. 
Since K = Debate, M ≠ Debate. 
Remaining options for M are Qz or Ch. 
Step 5: Check event uniqueness. 
After fixing: \[ L = Cd,\ K = Db \] The two remaining events Qz, Ch must be assigned to M and N in some order. Thus the assignments are: \[ (M = Qz,\ N = Ch) \quad\text{or}\quad (M = Ch,\ N = Qz) \] Both satisfy all constraints.
Total valid assignments: \[ \boxed{2} \] Final Answer: \(\boxed{2}\)