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2 player game with 13 positive integers

Source: 2017 Argentina OMA Finals L3 p1

January 16, 2023
combinatoricsgamegame strategy

Problem Statement

Nico picks 1313 pairwise distinct 3−3-digit positive integers. Ian then selects several of these 13 numbers, the ones he wants, and using only once each selected number and some of the operations addition, subtraction, multiplication and division (+,−,×,:+,-,\times ,:) must get an expression whose value is greater than 33 and less than 44. If he succeeds, Ian wins; otherwise, Nico wins. Which of the two has a winning strategy?
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