Reasoning — Coding-Decoding

The pattern followed is the direct concatenation of the alphabetical position of each letter. B is the 2nd letter, A is the 1st, T is the 20th. So, BAT -> 2120. C is the 3rd letter, A is the 1st, T is the 20th. So, CAT -> 3120. Applying the same pattern to 'DOG': D is the 4th letter. O is the 15th letter. G is the 7th letter. So, DOG -> 4157.

Let's analyze the given codes: 1. 'sky is blue' -> 'pa la sa' 2. 'blue and clear' -> 'sa na ka' 3. 'clear water is' -> 'ka ra pa' Comparing (1) and (2), the common word is 'blue' and the common code is 'sa'. So, 'blue' = 'sa'. Comparing (1) and (3), the common word is 'is' and the common code is 'pa'. So, 'is' = 'pa'. Comparing (2) and (3), the common word is 'clear' and the common code is 'ka'. So, 'clear' = 'ka'. Now, consider sentence (3): 'clear water is' -> 'ka ra pa'. We know 'clear' = 'ka' and 'is' = 'pa'. Therefore, the remaining word 'water' must correspond to the remaining code 'ra'. So, 'water' = 'ra'.

Let's analyze the pattern for 'SMART' -> 'TNDSU': S (19) + 1 = T (20) M (13) + 1 = N (14) A (1) + 3 = D (4) R (18) + 1 = S (19) T (20) + 1 = U (21) The pattern of shifts is +1, +1, +3, +1, +1. Applying the same pattern to 'HOUSE': H (8) + 1 = I (9) O (15) + 1 = P (16) U (21) + 3 = X (24) S (19) + 1 = T (20) E (5) + 1 = F (6) So, 'HOUSE' is coded as 'IPXTF'.

The pattern followed is the sum of the alphabetical positional values of the letters. C = 3, A = 1, T = 20. Sum = 3 + 1 + 20 = 24. D = 4, O = 15, G = 7. Sum = 4 + 15 + 7 = 26. Applying the same pattern to 'TIGER': T = 20 I = 9 G = 7 E = 5 R = 18 Sum = 20 + 9 + 7 + 5 + 18 = 59. So, 'TIGER' is coded as 59.

Let's analyze the given codes: 1. 'pen is blue' -> 'la pa ta' 2. 'blue ink bottle' -> 'ta ga ma' 3. 'ink is dark' -> 'ga pa sa' Comparing (1) and (2), the common word is 'blue' and the common code is 'ta'. So, 'blue' = 'ta'. Comparing (1) and (3), the common word is 'is' and the common code is 'pa'. So, 'is' = 'pa'. Comparing (2) and (3), the common word is 'ink' and the common code is 'ga'. So, 'ink' = 'ga'. Now, consider sentence (2): 'blue ink bottle' -> 'ta ga ma'. We know 'blue' = 'ta' and 'ink' = 'ga'. Therefore, the remaining word 'bottle' must correspond to the remaining code 'ma'. So, 'bottle' = 'ma'.

The pattern followed is the sum of the alphabetical positional values of the letters, multiplied by 2. For 'BAT': B = 2, A = 1, T = 20. Sum = 2 + 1 + 20 = 23. Code = 23 * 2 = 46. For 'CAT': C = 3, A = 1, T = 20. Sum = 3 + 1 + 20 = 24. Code = 24 * 2 = 48. Applying the same pattern to 'DOG': D = 4, O = 15, G = 7. Sum = 4 + 15 + 7 = 26. Code = 26 * 2 = 52. So, 'DOG' is coded as 52.

The pattern followed is the direct concatenation of the alphabetical positional values of each letter. For 'DREAM': D=4, R=18, E=5, A=1, M=13. Concatenating these gives 418513. For 'TIGER': T=20, I=9, G=7, E=5, R=18. Concatenating these gives 2097518. Applying the same pattern to 'HORSE': H=8 O=15 R=18 S=19 E=5 Concatenating these values gives 81518195. So, 'HORSE' is coded as '81518195'.

Let's determine the original numerical positions for 'APPLE': A = 1 P = 16 P = 16 L = 12 E = 5 Now, let's check the conditions: - The first letter is 'A', which is a vowel. - The last letter is 'E', which is also a vowel. According to Condition 3: "If both the first and last letters are vowels, then their codes are swapped." This means the code for the first letter 'A' (which is 1) will be used for the last letter 'E', and the code for the last letter 'E' (which is 5) will be used for the first letter 'A'. So, the coding for 'APPLE' will be: First letter 'A' gets the code of 'E' -> 5 Middle letters 'P', 'P', 'L' retain their original codes -> 16, 16, 12 Last letter 'E' gets the code of 'A' -> 1 Combining these, 'APPLE' is coded as 51616121.

Let's apply the given coding rules to each letter of 'EDUCATION': E: Vowel, coded as # D: Consonant, numerical position is 4 U: Vowel, coded as & C: Consonant, numerical position is 3 A: Vowel, coded as @ T: Consonant, numerical position is 20 I: Vowel, coded as $ O: Vowel, coded as % N: Consonant, numerical position is 14 Combining these, 'EDUCATION' is coded as #4&3@20$%14.

The pattern is that each letter in the word is shifted one position forward in the alphabet. A (+1) -> B P (+1) -> Q P (+1) -> Q L (+1) -> M E (+1) -> F Applying the same rule to 'GRAPE': G (+1) -> H R (+1) -> S A (+1) -> B P (+1) -> Q E (+1) -> F So, 'GRAPE' is coded as 'HSBQF'.

The code is the sum of the positional values of the letters in the alphabet (A=1, B=2, ... Z=26). For 'BAT': B(2) + A(1) + T(20) = 2 + 1 + 20 = 23. For 'CAT': C(3) + A(1) + T(20) = 3 + 1 + 20 = 24. Applying the same rule to 'DOG': D(4) + O(15) + G(7) = 4 + 15 + 7 = 26. So, 'DOG' is coded as 26.

We need to find the common words and their codes by comparing the given statements. 1. sky is blue -> pa la sa 2. blue and clear -> sa na ka 3. clear sky high -> ka ra pa Comparing (1) and (2): The common word is 'blue', and the common code is 'sa'. So, 'blue' = 'sa'. Comparing (1) and (3): The common word is 'sky', and the common code is 'pa'. So, 'sky' = 'pa'. Now, from statement (1) 'sky is blue' -> 'pa la sa', we know 'sky' is 'pa' and 'blue' is 'sa'. Therefore, the remaining word 'is' must correspond to the remaining code 'la'. So, the code for 'is' is 'la'.

The pattern is an alternating shift for each letter: - The 1st, 3rd, 5th, 7th... letters are shifted one position forward (+1). - The 2nd, 4th, 6th, 8th... letters are shifted two positions forward (+2). Let's apply this to 'CRICKET': C (+1) -> D R (+2) -> T I (+1) -> J C (+2) -> E K (+1) -> L E (+2) -> G T (+1) -> U So, 'CRICKET' is coded as 'DTJELGU'. Now, apply the same rule to 'FOOTBALL': F (+1) -> G O (+2) -> Q O (+1) -> P T (+2) -> V B (+1) -> C A (+2) -> C L (+1) -> M L (+2) -> N So, 'FOOTBALL' is coded as 'GQPVCCMN'.

First, determine the number of letters in 'TIGER'. 'TIGER' has 5 letters, which is an odd number. According to Condition 2, if a word contains an odd number of letters, each letter's code is decremented by 1. Positional values: T=20, I=9, G=7, E=5, R=18. Applying decrement by 1: T (20-1) -> 19 I (9-1) -> 8 G (7-1) -> 6 E (5-1) -> 4 R (18-1) -> 17 Concatenating these values, 'TIGER' is coded as '1986417'.

The pattern involves shifting letters based on whether they are vowels or consonants. - Vowels are shifted one position backward (-1). - Consonants are shifted one position forward (+1). Let's apply this to 'CRICKET': C (Consonant) -> C+1 = D R (Consonant) -> R+1 = S I (Vowel) -> I-1 = H C (Consonant) -> C+1 = D K (Consonant) -> K+1 = L E (Vowel) -> E-1 = D T (Consonant) -> T+1 = U So, 'CRICKET' is coded as 'DSHDLDU'. Now, apply the same rule to 'FOOTBALL': F (Consonant) -> F+1 = G O (Vowel) -> O-1 = N O (Vowel) -> O-1 = N T (Consonant) -> T+1 = U B (Consonant) -> B+1 = C A (Vowel) -> A-1 = Z (A-1 is Z in a cyclic alphabet. This is a common convention in coding-decoding.) L (Consonant) -> L+1 = M L (Consonant) -> L+1 = M So, 'FOOTBALL' is coded as 'GNNUCZMM'.

Let's find the pattern between the numbers and their corresponding letters. For 123 -> BDF: 1 -> B (B is the 2nd letter, 2*1 = 2) 2 -> D (D is the 4th letter, 2*2 = 4) 3 -> F (F is the 6th letter, 2*3 = 6) The pattern is: for each digit 'n', the corresponding letter is the letter at position (2 * n) in the alphabet. Let's check with 456 -> HJL: 4 -> H (H is the 8th letter, 2*4 = 8) 5 -> J (J is the 10th letter, 2*5 = 10) 6 -> L (L is the 12th letter, 2*6 = 12) The pattern holds. Now, apply this to 789: 7 -> (2 * 7) = 14th letter = N 8 -> (2 * 8) = 16th letter = P 9 -> (2 * 9) = 18th letter = R So, 789 is coded as 'NPR'.