Understanding the Coding Pattern

We are given two coded words and need to find the code for a specific letter.

• 'SHAT' is coded as '4956'
• 'ASHY' is coded as '3645'

The goal is to determine the code for the letter 'Y'.

Analyzing Letter and Code Correspondences

Let's compare the letters and digits in the given examples:

Word 1: S H A T

Code 1: 4 9 5 6

Word 2: A S H Y

Code 2: 3 6 4 5

We identify the letters common to both words ('S', 'H', 'A') and the digits common to both codes ('4', '5', '6'). This suggests a direct substitution cipher where these common letters correspond to these common digits, though not necessarily in the same order.

Deducing the Code for 'Y'

Consider the word 'ASHY' and its code '3645'.

• The letters are A, S, H, Y.
• The digits are 3, 6, 4, 5.

From the comparison above, we know that the letters 'A', 'S', and 'H' must correspond to three of the digits '4', '5', and '6'.

Therefore, the letter 'Y', which is unique to 'ASHY' among the compared letters, must correspond to the digit that is unique to the code '3645' when considering the mapping of A, S, H to 4, 5, 6.

The digits in '3645' are {3, 6, 4, 5}.

The digits common to both codes are {4, 5, 6}.

The digit unique to '3645' in this context is '3'.

Thus, the code for 'Y' must be '3'.

We can also deduce the code for 'T' from 'SHAT' = '4956'. The letters {S, H, A} correspond to {4, 5, 6}. The remaining letter is 'T' and the remaining digit is '9'. So, T=9.

Checking consistency:

• ASHY = 3645 implies Y = 3 and {A, S, H} = {6, 4, 5}
• SHAT = 4956 implies T = 9 and {S, H, A} = {4, 5, 6}

Both conditions are met. The code for 'Y' is '3'.

Final Answer

The code for 'Y' is 3.