Ten pirates find a sack of gold coins. When they try to divide up the gold (with equal shares for all) they find there is one coin left over. Upset, one of the pirates cries “Arg!" and leaves (with no gold). The remaining pirates again try to divide up the gold and this time they find to their horror there are two coins left over. So two more of the pirates cry “Arg!" and leave (with no gold). The remaining pirates divide up the gold and find, to their delight, that each gets an equal share and no coins are left over. What can we say about the number of gold coins in the sack? In particular, what is the smallest number of coins that make the story correct?

Ten pirates find a sack of gold coins. When they try to divide up the gold (with equal shares for all) they find there is one coin left over. Upset, one of the pirates cries “Arg!" and leaves (with no gold). The remaining pirates again try to divide up the gold and this time they find to their horror there are two coins left over. So two more of the pirates cry “Arg!" and leave (with no gold). The remaining pirates divide up the gold and find, to their delight, that each gets an equal share and no coins are left over. What can we say about the number of gold coins in the sack? In particular, what is the smallest number of coins that make the story correct?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

Ten pirates find a sack of gold coins. When they try to divide up the gold (with equal
shares for all) they find there is one coin left over. Upset, one of the pirates cries “Arg!"
and leaves (with no gold). The remaining pirates again try to divide up the gold and this
time they find to their horror there are two coins left over. So two more of the pirates
cry “Arg!" and leave (with no gold). The remaining pirates divide up the gold and find,
to their delight, that each gets an equal share and no coins are left over.
What can we say about the number of gold coins in the sack? In particular, what is
the smallest number of coins that make the story correct?

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