Can I cut the Gordian tnok? The impact of pronounceability, actual solvability, and length on intuitive problem assessments of anagrams Sascha Topolinski a,⇑ , Giti Bakhtiari b , Thorsten M. Erle b a University of Cologne, Germany b University of Wuerzburg, Germany article info Article history: Received 21 June 2015 Revised 28 September 2015 Accepted 26 October 2015 Keywords: Anagrams Problem solving Phonation Fluency abstract When assessing a problem, many cues can be used to predict solvability and solving effort. Some of these cues, however, can be misleading. The present approach shows that a feature of a problem that is actually related to solving difficulty is used as a cue for solving ease when assessing the problem in the first place. For anagrams, it is an established effect that easy-to-pronounce anagrams (e.g., NOGAL) take more time to being solved than hard-to-pronounce anagrams (e.g., HNWEI). However, when assessing an anagram in the first place, individuals use the feature of pronounceability to predict solving ease, because pro- nounceability is an instantiation of the general mechanism of processing fluency. Participants (total N = 536) received short and long anagrams and nonanagrams and judged solvability and solving ease intuitively without actually solving the items. Easy-to-pronounce letter strings were more frequently judged as being solvable than hard-to-pronounce letters strings (Experiment 1), and were estimated to require less effort (Experiments 2, 4–7) and time to be solved (Experiment 3). This effect was robust for short and long items, anagrams and nonanagrams, and presentation timings from 4 down to 0.5 s, and affected novices and experts alike. Spontaneous solutions did not mediate this effect. Participants were sensitive to actual solvability even for long anagrams (6–11 letters long) presented only for 500 ms. Ó 2015 Elsevier B.V. All rights reserved. 1. Introduction The solution of a problem starts with the initial assessment of whether a problem is solvable at all and how hard it would be to solve it (Ackerman & Thompson, 2014; Kruglanski et al., 2012), which can have strong emotional and motivational consequences, such as on learned helplessness or self-efficacy (Davis & Yates, 1982; Frankel & Snyder, 1978; Smith, 1996; Snyder, Smoller, Strenta, & Frankel, 1981). Intellectually, the formal assessment of problem solvability (cf., Entscheidungsproblem, Hilbert & Ackermann, 1928) was the driving force of the 20th century’s most productive mathematicians, such as Hilbert, Gödel, Turing, or Pen- rose (Davis, 1958). Triaging a problem as very hard to solve or even unsolvable (De Neys, Rossi, & Houdé, 2013; Stanovich, 2009) might lead to abandoning very important and actually solvable problems, like in the centuries-long frustrations in proving Fermat’s last theorem (Wiles, 1995). On the other side, endorsing an actually unsolvable problem as being solvable might lead to wasted intellectual effort (Kruglanski et al., 2012), such as for the classic problem of squaring the circle, which has been pursued for millennia until it was eventually proven impossible (Hardy & Wright, 1979). Various cues can be used for this initial assessment of solvabil- ity and solving difficulty. Besides actually engaging in solving the problem and monitoring the solving progress (Payne & Duggan, 2011), more immediate cues are one’s prior experiences with related problems (expertise, e.g., Novick & Sherman, 2008) and, most importantly, available features of the problem itself (Ackerman & Thompson, 2014). Of course, some of these features are valid, while others are invalid predictors. Moreover, within the valid cues used for problem assessment, some might be used correctly, while others might not. The idea of the present research is to show that there are valid cues of problem solvability that are used in the wrong predictive direction. Specifically, we will show that a feature of a problem that is actually related to solving difficulty is used as a proxy for solving ease when assessing the problem in the first place. This feature is pronounceability of anagrams. It is a well- established classic effect that easy-to-pronounce anagrams, such as NOGAL or OARLY, take more time to be solved than hard-to- pronounce anagrams, such as HNWEI or AOSLR (Dominowski, http://dx.doi.org/10.1016/j.cognition.2015.10.019 0010-0277/Ó 2015 Elsevier B.V. All rights reserved. ⇑ Corresponding author at: Department of Psychology, Social and Economic Cognition, University of Cologne, Richard-Strauß-Straße 2, 50931 Cologne, Germany. E-mail address: sascha.topolinski@uni-koeln.de (S. Topolinski). Cognition 146 (2016) 439–452 Contents lists available at ScienceDirect Cognition journal homepage: www.elsevier.com/locate/COGNIT