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Coding + Direction Hybrid

Introduction

Coding + Direction Hybrid समस्याएँ directional सम्बन्धों को प्रतीकों या छोटे वाक्यों में एन्कोड करती हैं (उदा., ‘A # B’ का अर्थ “A is North of B” होना) और फिर उन कोडित सम्बन्धों को movement या turns के साथ जोड़ती हैं। आपको पहले प्रतीकों को decode करना होगा, उन्हें स्थानिक सम्बन्धों या rotations में बदलना होगा, और फिर उन सम्बन्धों को संयोजित कर के प्रश्न का उत्तर देना होगा।

यह पैटर्न महत्वपूर्ण है क्योंकि कई प्रतियोगी परीक्षाएँ directional जानकारी को symbolic statements में संकुचित कर देती हैं ताकि जटिलता बढ़े और solver की decoding, relation-chaining और reversal-गलतियों से बचने की क्षमता परखा जा सके।

Pattern: Coding + Direction Hybrid

Pattern

मुख्य विचार: प्रत्येक कोड को एक ठोस directional कथन (cardinal या intercardinal) में अनुवाद करें, फिर decode किए हुए सम्बन्धों को step-by-step जोड़ें - प्रतीकों को vector offsets या facing rotations की तरह मानें।

व्यवहारिक नियम

  • पहले एक decoding legend बनाएं: हर symbol को एक स्पष्ट अर्थ दें (उदा., A # B → A is North of B)।
  • कोडित सम्बन्धों को तुरंत coordinate offsets या facing-rotations में बदलें (उदा., North = +y, East = +x, Right = +90°)।
  • रिश्तों को क्रमिक रूप से chain करें और जब reference बदलती हो तो relation को सही तरीके से invert करें (A north of B → B south of A)।
  • जब कोड संयोजित हों (उदा., P # Q $ R) तो stepwise expand करें: पहले P # Q decode करें, फिर Q $ R decode करें, और फिर P का R के सापेक्ष स्थान निकालें।
  • जैसे-जैसे आप decode करें, हर इकाई के लिये छोटा सा diagram बनाएं या symbolic coordinates असाइन करें ताकि directional गलतियाँ न हों।

Step-by-Step Example

Question

एक कोड में, ‘A # B’ का अर्थ है “A is North of B”, और ‘A $ B’ का अर्थ है “A is East of B”。 कथन ‘P # Q $ R’ P और R के बीच क्या बताता है?

Solution

  1. Step 1: प्रतीकों को decode करें

    ‘#’ = North of (Δy = +), ‘$’ = East of (Δx = +)।

  2. Step 2: P # Q decode करें

    P is North of Q → यदि Q = (0,0) तो P = (0, +a)।

  3. Step 3: Q $ R decode करें

    Q is East of R → यदि R = (0,0) तो Q = (+b, 0)।

  4. Step 4: posiciones मिलाएँ

    R = (0,0), Q = (+b, 0), P = (b, +a)।

  5. Step 5: P का R के सापेक्ष स्थान निकाले

    P = (b, +a) → x और y दोनों सकारात्मक → P R के सापेक्ष North-East में है।

  6. Final Answer:

    P is North-East of R

  7. Quick Check:

    दोनों components positive हैं → NE ✅

Quick Variations

1. प्रतीक जो facing/turns दर्शाते हैं (उदा., ‘A ⇒ B’ मतलब “A turns right and faces B”).

2. मिश्रित रिश्ते: position codes (north/east) + facing codes (left/right) को अलग-अलग हैंडल करें।

3. बहु-स्टेप चेन जैसे P # Q, Q # R, R $ S → P का S के सापेक्ष स्थान निकालना।

4. सशर्त कोड वाले बयानों (“If P # Q then …”) जो backtracking और logical deduction माँगते हैं।

Trick to Always Use

  • Step 1: हर symbol के लिए decoding legend बनाएँ और मैप करें।
  • Step 2: हर decode किये गए relation को तुरंत (Δx, Δy) offsets या degree rotation में बदलें।
  • Step 3: offsets को step-by-step जोड़ें; जब reference बदले तो relations को invert करना न भूलें।

Summary

Summary

  • हमेशा स्पष्ट रूप से symbol legend से शुरुआत करें।
  • कोडित सम्बन्धों को तुरंत directional या coordinate रूप में अनुवाद करें।
  • decode किये गए offsets को क्रमिक रूप से जोड़ें और आवश्यकता हो तो relations को reverse करें।
  • NE/NW/SE/SW की सहीता जांचने के लिए छोटे sketches बनाएं।

याद रखने के लिए उदाहरण:
यदि ‘#’ = North और ‘$’ = East, तो P # Q $ R → P is North-East of R।

Practice

(1/5)
1. In a code, '^' means 'is North of' and '&' means 'is East of'. What does 'P ^ Q & R' mean?
easy
A. P is North-East of R
B. P is South-East of R
C. P is North-West of R
D. P is South-West of R

Solution

  1. Step 1: Decode the symbols

    '^' = North of, '&' = East of.

  2. Step 2: Decode first relation

    P ^ Q → P is North of Q.

  3. Step 3: Decode second relation

    Q & R → Q is East of R.

  4. Step 4: Combine

    R at origin → Q is East of R, and P is North of Q → P is North-East of R.

  5. Final Answer:

    P is North-East of R → Option A

  6. Quick Check:

    Both North and East → NE ✅
Hint: Decode rightmost relation first (Q & R) then use it to place the left entity.
Common Mistakes: Reversing reference (treating Q as relative to P instead of to R).
2. If '@' means 'is West of' and '%' means 'is South of', what does 'P @ Q % R' mean?
easy
A. P is North-East of R
B. P is South-West of R
C. P is North-West of R
D. P is South-East of R

Solution

  1. Step 1: Decode symbols

    '@' = West of, '%' = South of.

  2. Step 2: Decode middle relation

    Q % R → Q is South of R (Q = (x, y-b)).

  3. Step 3: Apply left relation

    P @ Q → P is West of Q → P is West and South relative to R → South-West.

  4. Final Answer:

    P is South-West of R → Option B

  5. Quick Check:

    West (x↓) + South (y↓) → SW ✅
Hint: Place R at origin, map Q from R, then map P from Q.
Common Mistakes: Swapping the order of decoding (doing P @ Q first without referencing R).
3. In a code, '$' means 'is East of' and '*' means 'is South of'. What does 'X * Y $ Z' mean?
easy
A. X is North-East of Z
B. X is North-West of Z
C. X is South-East of Z
D. X is South-West of Z

Solution

  1. Step 1: Decode the symbols

    '$' = East of, '*' = South of.

  2. Step 2: Decode rightmost relation

    Y $ Z → Y is East of Z.

  3. Step 3: Apply left relation

    X * Y → X is South of Y. With Y east of Z, X is South-East of Z.

  4. Final Answer:

    X is South-East of Z → Option C

  5. Quick Check:

    East (x↑) + South (y↓) → SE ✅
Hint: Work right-to-left: place Z, then Y, then X.
Common Mistakes: Mixing up South vs North signs when combining offsets.
4. If '# ' means 'is North of' and '&' means 'is East of', what does 'M & N # O' imply?
medium
A. M is North-East of O
B. M is South-East of O
C. M is North-West of O
D. M is South-West of O

Solution

  1. Step 1: Decode symbols

    '&' = East of, '#' = North of.

  2. Step 2: Decode right relation

    N # O → N is North of O.

  3. Step 3: Apply left relation

    M & N → M is East of N. With N north of O, M is North-East of O.

  4. Final Answer:

    M is North-East of O → Option A

  5. Quick Check:

    N above O (y↑), M to right of N (x↑) → NE ✅
Hint: Place base (O), then N relative to O, then M relative to N.
Common Mistakes: Applying left relation before establishing the right relation's reference.
5. If '*' means 'is South of' and '&' means 'is West of', what does 'M * N & O' mean?
medium
A. M is North-East of O
B. M is North-West of O
C. M is South-East of O
D. M is South-West of O

Solution

  1. Step 1: Decode symbols

    '*' = South of, '&' = West of.

  2. Step 2: Decode right relation

    N & O → N is West of O.

  3. Step 3: Apply left relation

    M * N → M is South of N. With N west of O, M is South-West of O.

  4. Final Answer:

    M is South-West of O → Option D

  5. Quick Check:

    West (x↓) + South (y↓) → SW ✅
Hint: Map O → place N (west), then place M (south of N) to get SW.
Common Mistakes: Reading relations left-to-right without fixing reference positions first.

Mock Test

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