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UKMT Junior Mathematical Challenge, 2023

Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Amrita needs to select a new PIN. She decides it will be made up of four non-zero digits with the following properties: i) The first two digits and the last two digits each make up a two-digit number which is a multiple of 11. ii) The sum of all the digits is a multiple of 11. How many different possibilities are there for Amrita's PIN?

(A) $1$ (B) $2$ (C) $4$ (D) $8$ (E) $16$

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