Questions tagged [frobenius]

The Frobenius problem asks for the largest amount that cannot be obtained by using only coins of specified denominations.

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3answers
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Ten types of stamps

The country Dalgonia issues stamps of only ten different denominations: $134$, $135$, $136$, $137$, $138$, $139$, $140$, $141$, $142$, and $143$ cents. What is the largest amount of cents which ...
46
votes
5answers
6k views

A man possesses a large quantity of stamps

James Joseph Sylvester was one the greatest British mathematicians of the 19th century, who made many fundamental contributions to number theory, combinatorics, and invariant theory. In 1884, he ...
7
votes
3answers
487 views

Non-Pythagorean coins (Part 2)

To make payments, the Non-Pythagoreans use coins in three denominations of 999, 1000, and 1001 Oboloi. Some amounts of Oboloi do not allow any representation by these three denominations (for ...
4
votes
3answers
635 views

Non-Pythagorean coins (Part 1)

To make payments, the Non-Pythagoreans use coins in three denominations of 999, 1000, and 1001 Oboloi. What is the largest integer amount of Oboloi that can not be represented by using these three ...
5
votes
1answer
613 views

Pythagorean coins

To make payments, the Pythagoreans use coins in no more than three denominations. The three denominations are in whole Oboloi amounts, and the sum of the squares of the two smaller denominations ...