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Frey D, Johnson ED, & De Neys W (2017). Individual differences in conflict detection during reasoning. Quarterly Journal of Experimental Psychology, 71, 1188–1208. doi: 10.1080/17470218.2017.1313283 [ PubMed] [ CrossRef] [ Google Scholar] Psychology of learning and motivation (Vol. 26, pp. 125–173). Academic Press. doi: 10.1016/S0079-7421(08)60053-5. [ CrossRef] [ Google Scholar] Mata A, Ferreira MB, Voss A, & Kollei T (2017). Seeing the conflict: An attentional account of reasoning errors. Psychonomic Bulletin & Review, 24, 1980–1986. doi: 10.3758/s13423-017-1234-7 [ PubMed] [ CrossRef] [ Google Scholar]

The question really belongs more to the science of the mind than it does to mathematics and logic— it is about the assumptions we make, rather than whether or not we have the ability to solve the question.

Anyway, here are the other 2 questions:

De Neys W, Cromheeke S, & Osman M (2011). Biased but in doubt: Conflict and decision confidence. PloS one, 6( 1), e15954. [ PMC free article] [ PubMed] [ Google Scholar] Agnoli F, & Krantz DH (1989). Suppressing natural heuristics by formal instruction: The case of the conjunction fallacy. Cognitive Psychology, 21, 515–550. doi: 10.1016/0010-0285(89)90017-0 [ CrossRef] [ Google Scholar] De Neys W, & Bonnefon J-F (2013). The ‘whys’ and ‘whens’ of individual differences in thinking biases. Trends in Cognitive Sciences, 17, 172–178. doi: 10.1016/j.tics.2013.02.001 [ PubMed] [ CrossRef] [ Google Scholar] Thousands of students from MIT, Harvard, and Princeton had been put through the quiz, and you’d think that anyone in these prestigious universities would be able to solve this problem with an unerring ease. Not so fast. It turned out that more than 50% responded with the knee-jerk—incorrect—answer. The two systems that led to the choices. The analysis of variance was conducted on proportions to enable comparison with the findings of De Neys et al. (2013), who used an analysis of variance on percentages to compare standard and control problems. However, because the dependent variable is dichotomous (0 or 1), a mixed effects logistic regression (with subject as the random variable) is more appropriate and yielded comparable results. Specifically, participants were significantly more likely to respond accurately to isomorphic control questions than to standard variants, b = −3.73, odds ratio ( OR) = 41.57, χ 2 = 153.54, p< .001, 95% confidence interval ( CI) [0.01, 0.04]. That is, participants’ odds of answering the isomorphic control questions correctly was about 42 times more likely than answering the standard variants correctly.

For the recall response, a mixed effects logistic regression (with subject as the random variable) was conducted due to the dichotomous dependent variable (with or without “more than”), considering only those participants who wrote down an answer that could be coded as with or without the “more than” phrase (e.g., “don’t know” responses were excluded). Incorrect reasoners usually recalled the standard problem, but not the control, as containing “more than” (see Table 1), with this effect of condition significant, b = 3.02, odds ratio ( OR) = 20.44, χ 2 = 21.69, p< .001, 95% confidence interval ( CI) [5.74, 72.75]. Pennycook G, Fugelsang JA, & Koehler DJ (2012). Are we good at detecting conflict during reasoning? Cognition, 124, 101–106. doi: 10.1016/j.cognition.2012.04.004 [ PubMed] [ CrossRef] [ Google Scholar] As for the response confidence scores, the opinion judgments are reported here as proportions rather than percentages. There was a positive relationship between standard question confidence and standard question opinion judgments for incorrect reasoners, r(225) = .480, p< .001, such that incorrect reasoners who were less confident in their response were also less likely to think other reasoners could answer the standard question correctly. This strong relationship lends support to the notion that opinion judgments and response confidence scores are reflecting similar cognitive processes. Bourgeois-Gironde S, & Vanderhenst J-B (2009). How to open the door to System 2: Debiasing the Bat and Ball problem. In Watanabe S, Bloisdell AP, Huber L, & Young A (Eds.), Rational animals, irrational humans (pp. 235–252). Tokyo: Keio University Press. [ Google Scholar] Gangemi A, Bourgeois-Gironde S, & Mancini F (2015). Feelings of error in reasoning—in search of a phenomenon. Thinking & Reasoning, 21, 383–396. doi: 10.1080/13546783.2014.980755 [ CrossRef] [ Google Scholar]Klayman J, Soll JB, González-Vallejo C, & Barlas S (1999). Overconfidence: It depends on how, what, and whom you ask. Organizational Behavior and Human Decision Processes, 79, 216–247. doi: 10.1006/obhd.1999.2847 [ PubMed] [ CrossRef] [ Google Scholar] For the second and third samples, nine simple math problems were included between the experimental questions and the memory questions to serve as interference to limit recall and recognition based on working memory (see the Supplemental Materials). Neither math problems nor any other activity occurred between the De Neys et al. (2013) experimental and the memory questions for the first sample. Specifically, we started by testing 126 MTurk participants and then examined their data. We did not have a precise stopping rule for the sample size, but we decided from the outset to pause data collection after examining the data from an initial sample of MTurk participants. We noted poor memory performance by these initial participants. On the basis of our observations, we tested two additional samples of participants (one from MTurk and one from UCB), each approximately the same size as the initial sample (128 participants), and gave them the math problems to create interference.

Faul F, Erdfelder E, Lang A-G, & Buchner A (2007). G* Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39, 175–191. doi: 10.3758/BF03193146 [ PubMed] [ CrossRef] [ Google Scholar] Arkes HR, Christensen C, Lai C, & Blumer C (1987). Two methods of reducing overconfidence. Organizational Behavior and Human Decision Processes, 39, 133–144. doi: 10.1016/0749-5978(87)90049-5 [ CrossRef] [ Google Scholar] For recognition, all incorrect reasoners’ responses were included in the analyses because their answers came in the form of a multiple-choice forced response. A mixed effects logistic regression (with subject as the random variable) was again conducted due to the dichotomous dependent variable (with or without “more than”). Once again, incorrect reasoners usually recognized the standard problem, but not the control, as containing “more than” (see Table 1), with this effect of condition significant, b = 3.00, odds ratio ( OR) = 20.07, χ 2 = 50.34, p< .001, 95% confidence interval ( CI) [8.76, 45.94].De Neys W (2014). Conflict detection, dual processes, and logical intuitions: Some clarifications. Thinking & Reasoning, 20, 169–187. doi: 10.1080/13546783.2013.854725 [ CrossRef] [ Google Scholar] Mata A, & Ferreira MB (2018). Response: Commentary: Seeing the conflict: an attentional account of reasoning errors. Frontiers in Psychology, 9, 24. doi: 10.3389/fpsyg.2018.00024 [ PMC free article] [ PubMed] [ CrossRef] [ Google Scholar] Aczel B, Szollosi A, & Bago B (2016). Lax monitoring versus logical intuition: The determinants of confidence in conjunction fallacy. Thinking & Reasoning, 22, 99–117. doi: 10.1080/13546783.2015.1062801 [ CrossRef] [ Google Scholar]