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# Matchboxes and problem solving

## Problem

A psychologist puts a candle, matches, and thumbtacks on a table and brings participants into her lab to solve the following problem: attach the candle to the wall using only those materials. For half of the participants, the matches were spread out on the table next to the matchbox (the “Matchbox Empty” condition). For the other half of the participants, the matches were inside the matchbox (the “Matchbox Full” condition). Table $1$ shows the proportion of participants in each condition who correctly solved the problem (i.e., used the thumbtacks to attach the matchbox to the wall, then put the candle inside the matchbox).
Table $1$
Matchbox EmptyMatchbox Full
$.84$$.46$
Suppose the psychologist does a follow-up experiment in which there are three groups instead of two. The first two groups are the same as in the original experiment. In the third group, participants come into the room and see thumbtacks, a candle, a matchbox full of toothpicks, and matches spread out on the table. Table $2$ illustrates the proportion of individuals in each group who correctly solved the problem.
Table $2$
Matchbox EmptyMatchbox Full of MatchesMatchbox Full of Toothpicks
$.85$$.44$$.81$
The psychologist believes there will be a negative correlation between the ability to solve the problem accurately and the time it takes to solve the problem accurately. If that is the case, which group of participants would solve the problem fastest?