In a certain code language, "GRADUATE" is written as "2092623626722", then how will "ARIHANT" be written in that language?

In a certain code language, "GRADUATE" is written as "2092623626722". How will "ARIHANT" be written in that language?

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This is a pattern-recognition problem. We need to figure out how each letter becomes a number, then apply the same rule to "ARIHANT".

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Let's write out the word and the code:

Word: $\text{G-R-A-D-U-A-T-E}$ ($8$ letters)

Code: $2092623626722$

How do we split this long number into $8$ parts (one for each letter)?

Let's try: $20-9-26-23-6-26-7-22$ (This gives us $8$ segments)

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Now let's find each letter's position in the alphabet and compare with the code:

$\text{G} = 7^{\text{th}}$ letter $\rightarrow 20$

$\text{R} = 18^{\text{th}}$ letter $\rightarrow 9$

$\text{A} = 1^{\text{st}}$ letter $\rightarrow 26$

$\text{D} = 4^{\text{th}}$ letter $\rightarrow 23$

$\text{U} = 21^{\text{st}}$ letter $\rightarrow 6$

$\text{A} = 1^{\text{st}}$ letter $\rightarrow 26$

$\text{T} = 20^{\text{th}}$ letter $\rightarrow 7$

$\text{E} = 5^{\text{th}}$ letter $\rightarrow 22$

Notice: $7 + 20 = 27$, $18 + 9 = 27$, $1 + 26 = 27$, $4 + 23 = 27$

The pattern is: $\text{Code} = 27 - \text{(Letter Position)}$

This is the "reverse alphabet" pattern.

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Let's verify:

$\text{G: } 27 - 7 = 20$ ✓

$\text{R: } 27 - 18 = 9$ ✓

$\text{A: } 27 - 1 = 26$ ✓

$\text{D: } 27 - 4 = 23$ ✓

$\text{U: } 27 - 21 = 6$ ✓

$\text{A: } 27 - 1 = 26$ ✓

$\text{T: } 27 - 20 = 7$ ✓

$\text{E: } 27 - 5 = 22$ ✓

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Now let's code $\text{A-R-I-H-A-N-T}$ ($7$ letters):

$\text{A} = 1^{\text{st}}$ letter: $27 - 1 = 26$

$\text{R} = 18^{\text{th}}$ letter: $27 - 18 = 9$

$\text{I} = 9^{\text{th}}$ letter: $27 - 9 = 18$

$\text{H} = 8^{\text{th}}$ letter: $27 - 8 = 19$

$\text{A} = 1^{\text{st}}$ letter: $27 - 1 = 26$

$\text{N} = 14^{\text{th}}$ letter: $27 - 14 = 13$

$\text{T} = 20^{\text{th}}$ letter: $27 - 20 = 7$

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Combine all the codes: $26-9-18-19-26-13-7$

Written together: $269181926137$