Who broke the window?

Logic Level 4

A group of boys, all very close friends, were playing a team ball game in their street. One of the teams of 3 accidentally kicked the ball against a window of their neighbor's house, breaking the glass.

Hearing glass break, but not knowing exactly what had happened, or who was outside, the owner of the house, Sue, prepared to make her way outside to assess the situation, and to make sure that nobody was hurt. She immediately went to collect her first-aid kit, just in case, but it took her at least a minute to find it.

The ball had fallen back down outside, still intact, and Anton, Brian, and Calvin hadn't heard any immediate complaints about the window, so the 3 of them each decided to stay and continue playing with the ball.

Upon arriving outside, Sue recognizes Anton, Brian, and Calvin - now aware that they are being confronted about the window. They all suddenly look unnerved and somewhat ashamed for being party to what had happened moments ago. However, Sue was glad to see that everyone was unharmed, and treated all of them very kindly.

When Sue questioned them about who kicked the ball through the window, neither Anton, nor Brian, nor Calvin could bring themselves to lie to Sue, but none of the boys would ever tell on any of their friends, so Anton, Brian and Calvin each told Sue who it wasn't.

  • Anton: "It wasn’t me."
  • Brian: "It wasn’t Calvin."
  • Calvin: "It wasn’t me."

Given that only 1 boy could have kicked the ball, and that we know that Anton, Brian and Calvin are all telling the truth, who can we determine broke the window?

Anton Brian Calvin Someone else We can't determine who it was

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2 solutions

Jonathan Quarrie
Jun 24, 2017

This sneaky problem tests your ability to make a distinction between the group as a whole, the teams of 3, and the 3 boys - Anton, Brian, and Calvin. The use of the number 3 has been applied in multiple contexts in a deliberate attempt to confuse you (sorry) - Repetition of both the number 3 and the 3 boys' names is designed to anchor you to the idea that only the 3 boys exist in the group, despite there being evidence of multiple teams when the window was broken ('teams of 3' is plural). It is also important to understand our position for this problem as a solver, and separate ourselves from Sue's perspective, because we have more information than Sue.

Now that we know from our perspective that there were more than 3 boys in the group when the window was broken, we must include ' someone else ' as a possibility, even though 'someone else's actions aren't explicitly accounted for beyond the opening sentences.

You are then also being tested on whether you jump to a conclusion with the first (or most obvious) answer that suits the requirements, or whether you are assessing all possible singular answers.


A case study will show who it could have been.

Statement If it was Anton If it was Brian If it was Calvin If it was someone else
Anton: "It wasn't me." F a l s e \color{#D61F06}False T r u e \color{#20A900}True T r u e \color{#20A900}True T r u e \color{#20A900}True
Brian: "It wasn't Calvin." T r u e \color{#20A900}True T r u e \color{#20A900}True F a l s e \color{#D61F06}False T r u e \color{#20A900}True
Calvin: "It wasn't me." T r u e \color{#20A900}True T r u e \color{#20A900}True F a l s e \color{#D61F06}False T r u e \color{#20A900}True

With two cases showing all three statements as T r u e \color{#20A900}True , it could have been Brian or it could have been someone else .

Thus, we can’t determine who it was \boxed{\text{we can't determine who it was}} .


Sai Teja Uppili
Sep 26, 2019

Considering there are two teams, so the total children playing are 6. No data here suggested that which team is responsible for the broken window. So it could be Brian or a player from the other team. Thus, we can't determine that who broke the window.

There isn't any data on how many teams there are, or what type of game it is they're playing. But we can conclude that for it to be a team game, and for the culprit to be within one of the teams (plural), there must be at least two teams of 3 - Which does indeed mean that there must have been more than 3 boys playing this game when the window was broken.

We can't conclude precisely how many teams there were, or if there were also teams of other sizes in this unidentified game. However, you do capture the essence of this problem succinctly in your solution!

Jonathan Quarrie - 1 year, 8 months ago

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