The Guardian has published the solutions to a set of logic puzzles that challenge readers to determine how many people at a round table are telling the truth. The puzzles, created by Daniel Griller, use age-based statements to create logical contradictions. The scenarios involve three, seven, and 999 people seated at separate tables.
Three-Person Table Constraints
The first scenario places three individuals at a table. Each person makes a statement about their age relative to the others. The rules state that no two people are the same age. The goal is to find the highest and lowest possible number of truth-tellers.
In this setup, the oldest person must be lying. This is because they cannot be younger than anyone else at the table. Therefore, the maximum number of truth-tellers is two. An arrangement exists where the two younger individuals tell the truth about being younger than the oldest person.
Conversely, the youngest person must be telling the truth. They are younger than everyone else, so their statement holds. This means the minimum number of truth-tellers is one. In a scenario where the other two lie, only the youngest person speaks the truth.
Seven-Person Table Logic
The second puzzle expands the group to seven people. Each person claims to be younger than the person to their immediate left and younger than the person two seats to their right. The challenge is to find the greatest and smallest number of truth-tellers.
The two oldest people must be lying. They cannot be younger than everyone else. This rules out six or seven truth-tellers. The solution also eliminates five truth-tellers. If five people were telling the truth, the third oldest person would have to be among them. This creates a seating arrangement that leaves no valid spot for the fourth oldest person to also tell the truth.
It is possible for four people to tell the truth. The arrangement requires careful ordering of ages to satisfy the conditions for four individuals while forcing the others to lie. The youngest person must always be telling the truth. If everyone is seated in descending order of age, only the youngest person tells the truth. This sets the minimum number of truth-tellers at one.
999-Person Table Pattern
The final puzzle involves 999 people. Each person states they are younger than the person three seats to their left and older than the person three seats to their right. This complex scenario uses a coloring pattern to simplify the logic. The seats are divided into three groups: gold, silver, and bronze.
Each person makes a statement about people in seats of the same color. The youngest and oldest person in each color group must be lying. This means not everyone in a group can tell the truth. However, it is possible for every other person in each group to tell the truth. This is achieved by seating them so that age increases as you move clockwise around the table within that color group.
Applying this pattern to all three groups results in 993 truth-tellers. This is calculated by subtracting the six liars (two from each color group) from the total of 999 people. The maximum number of truth-tellers is therefore 993.
The minimum number of truth-tellers is zero. If the 999 people are seated in descending order of age as you move clockwise, every statement becomes false. The youngest person is not younger than the person three seats to their left. The oldest person is not older than the person three seats to their right. This creates a scenario where everyone is lying.
These puzzles demonstrate how logical constraints can limit the number of true statements in a group. The solutions rely on identifying the positions of the oldest and youngest individuals in specific subsets of the group.
Source: The Guardian
