Weighing designs to detect a single counterfeit coin

In this article, we discuss at length a combinatorial problem which has been of historic interest. It has appeared as a puzzle in several different versions with varying degrees of difficulty. It can be simply stated as follows: We are given a number of coins which are otherwise identical except that there may be at most one fake coin among them which is either slightly heavier or slightly lighter than the other genuine coins. Using only a two-pan weighing balance, we must devise a weighing scheme to identify the counterfeit coin and determine whether it is heavier or lighter (or declare that all coins are normal). We construct both sequential and non-sequential (that is, simultaneously declared) weighing plans for any given number of coins containing at most one fake coin using the minimum number of weighings needed.     

Comparison of computed tomography and chest radiography in the detection of rib fractures in abused infants

PURPOSE: Chest radiographs (CXR) are the standard method for evaluating rib fractures in abused infants. Computed tomography (CT) is a sensitive method to detect rib fractures. The purpose of this study was to compare CT and CXR in the evaluation of rib fractures in abused infants. METHODS: This retrospective study included all 12 abused infants identified from 1999 to 2004 who had rib fractures and both CXR and CT (8 abdomen CTs, 4 chest CTs). CT exams had been performed for clinical indications, and were obtained within one day of the CXR. Studies were reviewed by two pediatric radiologists to determine the number, locations, and approximate ages of the rib fractures. A total of 225 ribs were completely (192) or partially (33) seen by CT, and the matched ribs on CXR were used for the analysis. RESULTS: The mean patient age was 2.5 months (1.2-5.6), with seven females and five males. While 131 fractures were visualized by CT, only 79 were seen by CXR (p<.001). One patient had fractures only seen by CT. There were significantly (p<.05) more early subacute (24 vs. 4), subacute (47 vs. 26), and old fractures (4 vs. 0) seen by CT than by CXR. Anterior (42 vs. 11), anterolateral (21 vs. 12), posterolateral (9 vs. 3) and posterior (39 vs. 24) fractures were better seen by CT than by CXR (p<.01). Bilateral fractures were detected more often by CT (11) than by CXR (6). CONCLUSIONS: While this study group is small, these findings suggest that CT is better than CXR in visualizing rib fractures in abused infants.     

Deaf children's understanding of beliefs and desires

Twenty-two children (5-12 year old) who were profoundly, prelingually deaf were given two tests designed to tap their 'theory of mind', that is, their ability to attribute independent mental states to other people. The tests were versions of Baron-Cohen, Leslie, and Frith's Sally-Anne task and of Baron-Cohen's breakfast task. Seventy percent of the children were successful on all questions requiring belief attribution, a considerably and significantly larger percentage than the 29% obtained by Peterson and Siegal for a similar sample, though it is still lower than would be expected on the basis on chronological age. Children were universally successful on questions requiring the attribution of desire. We discuss implications of the findings.     

Unanticipated problems in the United States child protection system

While the United States child protection system is widely recognized as probably the most sophisticated and wide-ranging in the world, it nevertheless has some inherent problems. This article addresses some of the negative effects of mandatory reporting and the lack of fit of a short-term crisis intervention treatment approach for a substantial proportion of the protective services population. Reporting may have detrimental effects on the client-reporter relationship. Further, over half of the cases investigated are not substantiated. Of concern are the impact on innocent families of being investigated and the waste of scarce worker resources on investigation. While some protective services families are well suited to a crisis intervention model, a large number are multiproblem families who are always in crisis and families with chronic problems for whom crisis intervention is totally inadequate. Furthermore, because of high caseload size, workers are often not available to intervene after they have investigated the case. The problems described have been exacerbated by funding cutbacks under the current United States administration. The child protection system, along with other social welfare programs, is at risk for being dismantled by the Reagan administration.     

Identifying determinants of risk of sexual victimization of youth: a multivariate approach

The present study argues that a greater understanding of the factors which contribute to a youth's sexual victimization is likely to not only be based on what we know about the youths who are victimized but also on comparative information on youths who are not. Selected social background variables from a sample of young victims (n = 20) and nonvictims (n = 21) representing a population of youths with histories of antisocial behavior were compared. Using stepwise discriminant analysis several factors relating to youths' home environment significantly discriminated victims from nonvictims. The results suggest that the probability of being sexually victimized is increased when the home environment is unstable and lacks adequate control over youths' activities. The need for improved research methodologies to achieve better identification of determinants of risk is discussed. Multivariate assessment of social, situational, and personal factors of victims and nonvictims is recommended as a potentially promising approach for improving current rape prevention efforts.     

Diagrams and illustrations as aids to problem solving

The psychological literature relating to factors which should be taken into account in the design of illustrations and pictorial instructions as aids to problem solving is reviewed. The problem solver can invoke a wide range of strategies for using pictorial materials to achieve his goal, although pictorial instructions which indicate how to perform actions place a tighter constraint on the choice of strategy than illustrations showing only states to be attained. The designer must make his graphics compatible with as wide a range of strategies for using them as possible while building on the knowledge the problem solver already possesses.The author now works for the Post Office Telecommunications Systems Strategy Department, 88 Hills Road, Cambridge.