Most coin value with no exact dollar possible

Question

Using only US pennies, nickels, dimes and quarters, what is the largest total amount you can carry such that no selection of your coins adds up to exactly one dollar?

Short answer

$1.19. For example one quarter, nine dimes and four pennies: with only four pennies the cents must come from multiples of 5, and the quarter-plus-dimes amounts are $25+10k$ or $10k$ , never $100$ , while no nickel is allowed. An exhaustive search over coin counts confirms $119$ cents is the maximum.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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