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, 2011

Number theory Difficulty 2.0 Junior Prove it Canada

A set $S$ consists of all two-digit numbers such that:
- no number contains a digit of 0 or 9, and
- no number is a multiple of 11.
(a) Determine how many numbers in $S$ have a 3 as their tens digit.
(b) Determine how many numbers in $S$ have an 8 as their ones digit.
(c) Determine how many numbers are in $S$ .
(d) Determine the sum of all the numbers in $S$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.