In a certain code language, "is uc he bh kr" means "Lucky likes to dance freely"; "ha by lm kr op" means "Dance can be a hobby"; "he id ac kr bh" means "Lucky teaches dance to kids"; and "kr id bh tw uc" means "Kids dance freely with Lucky". In this language, how can the sentence "Lucky likes to dance with kids" be coded?

Introduction / Context:
This is a multi sentence coding decoding problem where you must decode several words simultaneously using overlapping information. The target is to encode the sentence "Lucky likes to dance with kids" using the same code language defined in the four given statements. This tests both logical reasoning and careful tracking of word code pairs.

Given Data / Assumptions:
Sentence 1: "is uc he bh kr" → "Lucky likes to dance freely".
Sentence 2: "ha by lm kr op" → "Dance can be a hobby".
Sentence 3: "he id ac kr bh" → "Lucky teaches dance to kids".
Sentence 4: "kr id bh tw uc" → "Kids dance freely with Lucky".
We assume each code token consistently represents the same English word across all sentences.

Concept / Approach:
We identify repeated words like "Lucky", "dance", "kids", "freely" and "are" equivalents across sentences and match them to repeating codes. Then we decode the remaining words by elimination. Finally, we construct the required sentence in English and replace each word with its code in the correct order.

Step-by-Step Solution:
1. "Dance" appears in all four sentences, and the code "kr" appears in all four coded lines. So kr → dance. 2. "Lucky" appears in sentences 1, 3 and 4. The common codes among their lines are bh and kr. kr is already dance, so bh → Lucky. 3. "Freely" appears in sentences 1 and 4. After removing known codes (bh for Lucky and kr for dance), the remaining codes in sentence 1 are is, uc, he and in sentence 4 are id, tw, uc. The only common code is uc, so uc → freely. 4. "Kids" appears in sentences 3 and 4. Removing kr (dance) and bh (Lucky) from both, the overlap between "he id ac" and "id tw uc" is id. Hence id → kids. 5. In sentence 3, "Lucky teaches dance to kids" = he id ac kr bh. We already know bh → Lucky, kr → dance, id → kids, leaving he and ac for "teaches" and "to" in some order. 6. In sentence 1, "Lucky likes to dance freely" = is uc he bh kr. We know uc → freely, bh → Lucky, kr → dance. Thus "likes" and "to" correspond to is and he. Since he already appears in the sentence about "teaches" and "to", it is natural to assign he → to and ac → teaches, leaving is → likes. 7. "With" appears only in sentence 4: "Kids dance freely with Lucky" = kr id bh tw uc. All words except "with" now have codes (kr, id, bh, uc). So tw → with. 8. Now encode "Lucky likes to dance with kids": Lucky → bh, likes → is, to → he, dance → kr, with → tw, kids → id. So the full code is "bh is he kr tw id".

Verification / Alternative check:
Substitute these mappings back into all given sentences to confirm consistency: each English sentence is reconstructed correctly with no contradictions. When we decode "bh is he kr tw id", we read "Lucky likes to dance with kids" exactly, which matches the target.

Why Other Options Are Wrong:
Option "he kr op id uc tw" contains op and omits bh, which we already know must represent "Lucky". Option "ac tw op bh uc id" also includes op, a code that never appears in a context matching "likes" or "to" in the correct order. Both fail to translate back to the target sentence correctly.

Common Pitfalls:
It is easy to mix up roles of he, is and ac, or to forget to remove already identified codes when searching for overlaps. Careful stepwise elimination and writing a mapping table at each stage avoids confusion and ensures that the final code matches the intended sentence exactly.

Final Answer:
The sentence "Lucky likes to dance with kids" is coded as bh is he kr tw id.