Posted Content•
Chameleon Coins
TL;DR: In this article, a chameleon coin can mimic a fake or a real coin, and it can choose which coin to mimic for each weighing independently, and the task is to use a balance to find two real coins one of which has to be fake.
Abstract: We discuss coin-weighing problems with a new type of coin: a chameleon A chameleon coin can mimic a fake or a real coin, and it can choose which coin to mimic for each weighing independently We consider a mix of $N$ coins that include exactly two non-real coins: one fake and one chameleon The task is to use a balance to find two coins one of which has to be fake We find bounds for the number of coins for which we can find a solution in a given number of weighings We also introduce an important idea of solution scaling
Citations
More filters
Posted Content•
[...]
TL;DR: In this article, a new type of coin called the alternator is introduced, which can pretend to be either a real or a fake coin (which is lighter than a real one).
Abstract: We introduce a new type of coin: \textit{the alternator} The alternator can pretend to be either a real or a fake coin (which is lighter than a real one) Each time it is put on a balance scale it switches between pretending to be either a real coin or a fake one In this paper, we solve the following problem: You are given $N$ coins that look identical, but one of them is the alternator All real coins weigh the same You have a balance scale which you can use to find the alternator What is the smallest number of weighings that guarantees that you will find the alternator?
2 citations
Posted Content•
TL;DR: Given the total number of coins and the starting state of the fake coin, the smallest number of weighings needed to identify thefake coin is calculated and an oblivious optimal strategy is provided for this number of weighsings.
Abstract: As in many coin puzzles, we have several identical-looking coins, with one of them fake and the rest real. The real coins weigh the same. Our fake coin is special in that it can change its weight. The coin can pretend to be a real coin, a fake coin that is lighter than a real one, and a fake coin that is heavier than a real one. In addition to this, each time the coin is on the scale, it changes its weight in a predetermined fashion.
In this paper, we seek to find our fake coin using a balance scale and the smallest number of weighings.
We consider different possibilities for the fake coin. We discuss coins that change weight between two states or between three states. The 2- state coin that changes weight from lighter to real and back has been studied before, so we concentrate on the 2-state coin that changes weight from lighter to heavier, and back. We also study the 3-state coin, which changes its weight from lighter to heavier to real, and back to lighter.
Given the total number of coins and the starting state of the fake coin, we calculate the smallest number of weighings needed to identify the fake coin. We provide an oblivious optimal strategy for this number of weighings. We also discuss what happens if the starting state is not known or mixed. In such cases, adaptive strategies are often more powerful than oblivious ones.
1 citations
Posted Content•
[...]
TL;DR: There are fun parallels between coin-weighing puzzles and knights, and it is established that knights and coins have similar properties.
Abstract: We establish fun parallels between coin-weighing puzzles and knights-