Which letter cluster can replace the question mark (?) to complete the given series?
HDZH, IFWL, ?, KJQT, LLNX
Letter Series Pattern Explanation
The question asks us to identify the correct letter cluster to replace the question mark (?) in the given series: HDZH, IFWL, ?, KJQT, LLNX. To solve this, we need to find a consistent pattern governing the progression of letters within each position of the clusters.
We can analyze the pattern by looking at each position separately:
Position-wise Pattern Analysis
Let's examine the letters at each position across the sequence:
- 1st Position: H, I, ?, K, L
- 2nd Position: D, F, ?, J, L
- 3rd Position: Z, W, ?, Q, N
- 4th Position: H, L, ?, T, X
Step-by-Step Cluster Calculation
We will determine the rule for each position:
-
First Letter Pattern:
- H to I is a step of +1 (H + 1 = I).
- I to the next letter is a step of +1. So, I + 1 = J.
- J + 1 = K.
- K + 1 = L.
-
Second Letter Pattern:
- D to F is a step of +2 (D + 2 = F).
- F to the next letter is a step of +2. So, F + 2 = H.
- H + 2 = J.
- J + 2 = L.
-
Third Letter Pattern:
- Z to W is a step of -3 (Z - 3 = W).
- W to the next letter is a step of -3. So, W - 3 = T.
- T - 3 = Q.
- Q - 3 = N.
-
Fourth Letter Pattern:
- H to L is a step of +4 (H + 4 = L).
- L to the next letter is a step of +4. So, L + 4 = P.
- P + 4 = T.
- T + 4 = X.
Combining the letters we found for each position (J, H, T, P), the missing letter cluster is JHTP.
Completed Series Verification
The completed series is: HDZH, IFWL, JHTP, KJQT, LLNX.
Let's verify the patterns:
| Position | Rule | Calculation | Result |
|---|---|---|---|
| 1st | +1 | H+1=I, I+1=J, J+1=K, K+1=L | J |
| 2nd | +2 | D+2=F, F+2=H, H+2=J, J+2=L | H |
| 3rd | -3 | Z-3=W, W-3=T, T-3=Q, Q-3=N | T |
| 4th | +4 | H+4=L, L+4=P, P+4=T, T+4=X | P |
The identified patterns correctly yield the cluster JHTP.
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