1. Commenting on the सूत्रम् 2-2-2 अर्धं नपुंसकम्‌ (used in step 2) the सिद्धान्तकौमुदी says – क्लीबे किम्‌? (ग्रामस्यार्ध: =) ग्रामार्ध:। Please explain.
Answer: Why does the सूत्रम् 2-2-2 अर्धं नपुंसकम्‌ specify the condition नपुंसकम्‌? Consider the example (ग्रामस्यार्ध: =) ग्रामार्ध: – a part (not exactly half) of the village.

(Note: When used in the neuter gender ‘अर्ध’ means ‘exactly half’ while used in the masculine gender it means ‘a part.’)

In the example ग्रामार्ध:, ‘अर्ध’ is used in the masculine – and hence does not mean ‘(exactly) half.’ Therefore the सूत्रम् 2-2-2 अर्धं नपुंसकम्‌ does not apply. Instead a षष्ठीसमास: is formed using the सूत्रम् 2-2-8 षष्ठी to give the form (ग्रामस्यार्ध: =) ग्रामार्ध:।

If the condition नपुंसकम्‌ were not to be specified in the सूत्रम् 2-2-2 अर्धं नपुंसकम्‌ then it would apply in this example too resulting in the undesired form अर्धग्राम: ।

2. Commenting further on the same सूत्रम् the सिद्धान्तकौमुदी says – द्रव्यैक्य एव। अर्धं पिप्पलीनाम्‌। Please explain.
Answer: द्रव्यैक्य एव – The सूत्रम् 2-2-2 अर्धं नपुंसकम्‌ applies only when the substance/thing consisting of parts is singular. Consider the example अर्धं पिप्पलीनाम्‌ – half of the (many) peppers. Since पिप्पलीनाम्‌ is not singular, the सूत्रम् 2-2-2 cannot be used to form a compound for अर्धं पिप्पलीनाम्‌।

3. Where has the सूत्रम् 2-3-37 यस्य च भावेन भावलक्षणम्‌ been used in the verses?
Answer: The सूत्रम् 2-3-37 यस्य च भावेन भावलक्षणम्‌ has been used in the form अर्धरात्रे (पुंलिङ्ग-प्रातिपदिकम् ‘अर्धरात्र’, सप्तमी-एकवचनम्) as well as the corresponding participle गते (प्रातिपदिकम् ‘गत’, पुंलिङ्गे सप्तमी-एकवचनम्)।

As per the सूत्रम् 2-3-37 यस्य च भावेन भावलक्षणम्‌ – A seventh case affix (‘ङि’, ‘ओस्’, ‘सुप्’) is used following a प्रातिपदिकम् (nominal stem) which denotes the one (agent/object) whose action (the timing of which is known) gives an indication of (the timing of) another action.
Note: In the present example, the action of ‘passing’ (expressed by गते) performed by the agent ‘mid-night’ (expressed by अर्धरात्रे) gives an indication of the timing of another action which is that of ‘giving up’ (expressed by जहौ।) Hence as per the सूत्रम् 2-3-37 यस्य च भावेन भावलक्षणम्‌, ‘अर्धरात्र’ – which denotes the agent of the indicating action of ‘passing’ – takes a seventh case affix.

Note: The action (लक्षण-क्रिया) in the absolute clause is generally expressed by using a participle ending in a कृत् affix. This participle (here ‘गत’) – being in grammatical agreement with the प्रातिपदिकम् (here the subject ‘अर्धरात्र’) which denotes the agent/object of the action – also takes the seventh case affix.

4. Which सूत्रम् justifies the तृतीया-तत्पुरुष: compound विवासनातुरः?
Answer: The तृतीया-तत्पुरुष: compound विवासनातुरः is justified by the सूत्रम् 2-1-32 कर्तृकरणे कृता बहुलम्‌ – A पदम् ending in a third case affix – denoting either the agent or the instrument of the action – variously compounds with (a syntactically related पदम् composed by adding a सुँप् affix to) a term ending in a कृत् affix (ref. 3-1-93 कृदतिङ्) and the resulting compound gets the designation तत्पुरुष:।

Here विवासनातुरः = विवासनेनातुरः। ’विवासन’ – exile (of his beloved son) is the cause/reason for आतुरः – (being) distressed.

बहुलग्रहणं सर्वोपाधिव्यभिचारार्थम्‌। The mention of बहुलम्‌ in this सूत्रम् tells us that all conditions may be relaxed. Hence sometimes we do see compounding taking place even when the condition कर्तृकरणे is not satisfied. In the present example, the third case affix used in विवासनेन denotes the हेतु: (cause/reason) and not the doer or the agent. But still compounding has taken place.

5. Can you spot the affix ‘कि’ in the verses?
Answer: The कृत् affix ‘कि’ occurs in the form संनिधौ (पुंलिङ्ग-प्रातिपदिकम् ‘संनिधि’, सप्तमी-एकवचनम्) – derived from the verbal root √धा (डुधाञ् धारणपोषणयोः | दान इत्यप्येके #३. ११) preceded by the उपसर्गौ ’सम्’ and ‘नि’।

संनिधानम् = संनिधि: = proximity

सम् नि धा + कि । By 3-3-92 उपसर्गे घोः किः – Following a verbal root which has the designation ‘घु’ (ref. 1-1-20 दाधा घ्वदाप्) and is in conjunction with a उपसर्ग:, the affix ‘कि’ may be used to denote either (i) the sense of the verbal root as having attained to a completed state or (ii) any कारक: except the agent of the action, provided the word so derived is a proper name.
= सम् नि धा + इ । अनुबन्ध-लोप: by 1-3-8 लशक्वतद्धिते and 1-3-9 तस्य लोपः।
= सम् नि ध् + इ = सम् नि धि । By 6-4-64 आतो लोप इटि च।
Note: ’सम् नि’ is compounded with ‘धि’ using the सूत्रम् 2-2-19 उपपदमतिङ्।
= संनिधि । By 8-3-23 मोऽनुस्वारः।
= संनिधि/सन्निधि । By 8-4-59 वा पदान्तस्य।
’संनिधि/सन्निधि’ gets प्रातिपदिक-सञ्ज्ञा by 1-2-46 कृत्तद्धितसमासाश्च।
Note: Words ending in the affix ‘कि’ derived using the सूत्रम् 3-3-92 are used in the masculine gender.

6. How would you say this in Sanskrit?
“Even after half the night had passed I did not get sleep.”
Answer: अर्धरात्रे गते अपि अहम् निद्राम् न लब्धवान्/लब्धवती = अर्धरात्रे गतेऽप्यहं निद्रां न लब्धवान्/लब्धवती ।

Easy questions:
1. Where has the सूत्रम् 3-1-55 पुषादिद्‍युताद्‍यॢदितः परस्मैपदेषु been used in the verses?
Answer: The सूत्रम् 3-1-55 पुषादिद्‍युताद्‍यॢदितः परस्मैपदेषु has been used in the verses in the form उपागमत् – derived from the verbal root √गम् (गमॢँ गतौ १. ११३७).

Please refer to the following post for derivation of the form अगमत् – http://avg-sanskrit.org/2012/05/07/अन्वगमत्-3as-लुँङ्/

’उप’ and ‘आङ्’ are the उपसर्गौ (ref. 1-4-59 उपसर्गाः क्रियायोगे, 1-4-80 ते प्राग्धातोः।)
उप आङ् + अगमत् = उप आ + अगमत् । अनुबन्ध-लोप: by 1-3-3 हलन्त्यम and 1-3-9 तस्य लोपः।
= उपागमत् । By 6-1-101 अकः सवर्णे दीर्घः (applied twice).

2. Which सूत्रम् prescribes the substitution ‘औ’ in the form जहौ?
Answer: The सूत्रम् 7-1-34 आत औ णलः prescribes the substitution ‘औ’ in the form जहौ – derived from the verbal root √हा (ओँहाक् त्यागे ३.९).

Please see the following post for derivation of the form जहौ – http://avg-sanskrit.org/2012/01/12/जहौ-3as-लिँट्/