A364607 Denominations of a 4-coin system that returns the fewest coins in change on average.

1, 5, 18, 25

Offset

1,2

Comments

In 1995, Thomas Young, along with students Jeff Greenfield, Joe Culbert, and David Raabe, explored the idea of the best 4-coin system for making change for a dollar. They assumed that each value for change (from 1 cent to 99 cents) was equally likely and, using an original Turbo Pascal program, calculated the average number of coins returned for every possible set of 4 coin denominations. Their result was announced via the essay, "Change the Dime not the Dollar."

The average number of coins required to return 1..99 cents is A339333(99,4)/99 = 389/99. - Pontus von Brömssen, Aug 13 2023

Links

Table of n, a(n) for n=1..4.

Thomas Young, A Turbo Pascal program to find the optimal coin system.

Thomas Young, Change the Dime Not the Dollar.

Crossrefs

Cf. A208953, A339333, A366013.

Sequence in context: A345912 A022142 A078648 * A035338 A055371 A034098

Adjacent sequences: A364604 A364605 A364606 * A364608 A364609 A364610

Keyword

nonn,full,fini

Author

Thomas Young, Aug 06 2023

Status

approved