In many Web-based applications, there are incentives for a user to sign up for more than one account, under false names. By doing so, the user can send spam e-mail from an account (which will eventually cause the account to be shut down); distort online ratings by rating multiple times (in particular, she can inflate her own reputation ratings); indefinitely continue using a product with a free trial period; place shill bids on items that she is selling on an auction site; engage in falsename bidding in combinatorial auctions; etc. All of these behaviors are highly undesirable from the perspective of system performance. While CAPTCHAs can prevent a bot from automatically signing up for many accounts, they do not prevent a human from signing up for multiple accounts. It may appear that the only way to prevent the latter is to require the user to provide information that identifies her in the real world (such as a credit card or telephone number), but users are reluctant to give out such information. In this paper, we propose an alternative approach. We investigate whether it is possible to design an automated test that is easy to pass once, but difficult to pass a second time. Specifically, we design a memory test. In our test, items are randomly associated with colors (“Cars are green.”). The user first observes all of these associations, and is then asked to recall the colors of the items (“Cars are...?”). The items are the same across iterations of the test, but the colors are randomly redrawn each time (“Cars are blue.”). Therefore, a user who has taken the test before will occasionally accidentally respond with the association from the previous time that she took the test (“Cars are...? Green!”). If there is significant correlation between the user’s answers and the correct answers from a previous iteration of the test, then the system can decide that the user is probably the same, and refuse to grant another account. We present and analyze the results of a small study with human subjects. We also give a game-theoretic analysis. In the appendix, we propose an alternative test and present the results of a small study with human subjects for that test (however, the results for that test are quite negative).