CAPTCHAs represent an important pillar in the web security domain. Yet, current CAPTCHAs do not fully meet the web security requirements. Many existing CAPTCHAs can be broken using automated attacks based on image processing and machine learning techniques. Moreover, most existing CAPTCHAs are completely vulnerable to human-solver relay attacks, whereby CAPTCHA challenges are simply outsourced to a remote human solver. In this paper, we introduce a new class of CAPTCHAs that can not only resist automated attacks but can also make relay attacks hard and detectable. These CAPTCHAs are carefully built on the notions of dynamic cognitive games (DCG) and emerging images (EI), present in the literature. While existing CAPTCHAs based on the DCG notion alone (e.g., an object matching game embedded in a clear background) are prone to automated attacks and those based on the EI notion alone (e.g., moving text embedded in emerging images) are prone to relay attacks, we show that a careful amalga...