The Plurality problem -introduced by Aigner [1] -has many variants. In this article we deal with the following version: suppose we are given n balls, each of them colored by one of three colors. A plurality ball is one such that its color class is strictly larger than any other color class. Questioner wants to find a plurality ball as soon as possible or state there is no, by asking triplets (or k-sets, in general), while Adversary partition the triplets into color classes as

Summary Background The addition of cisplatin or cetuximab to radiotherapy in patients with locally advanced squamous cell carcinoma of the head and neck (SCCHN) has significantly improved the outcome. While the superiority of cisplatin over cetuximab in combination with radiotherapy has been shown in a definitive setting, we set out to compare postoperative chemoradiotherapy with cisplatin to radioimmunotherapy with cetuximab and radiotherapy alone within the Austrian head and neck cancer registry of the Working Group on Pharmaceutical Tumor Treatment (AGMT) study group. Material and methods In the AGMT head and neck cancer registry, data of 557 patients with SCCHN from five Austrian cancer centers were prospectively collected between 2012 and 2017. Of these patients 120 received postoperative chemoradiotherapy with cisplatin, 26 patients received postoperative radioimmunotherapy with cetuximab and 56 patients were treated with adjuvant radiotherapy only. Patient characteristics, stage of disease, details on treatment as well as survival were analyzed by a chart-based review. Results In patients treated with postoperative radiotherapy the addition of cisplatin significantly improved progression-free survival (PFS) and overall survival (OS) compared to cetuximab (PFS 84.2 months vs. 17.0 months, p = 0.04, OS not reached vs. 46.0 months, p = 0.02) and PFS compared to radiotherapy alone (PFS 84.2 months vs. 28.5 months, p < 0.01). Patients treated with cetuximab were significantly older and had a worse performance score than patients receiving cisplatin or radiotherapy alone. Conclusion This study confirmed the importance of multimodal treatment concepts in patients with locally advanced SCCHN. Postoperative cetuximab might be an option in patients not eligible for high-dose cisplatin but cisplatin should remain the standard of care.

We investigate the following version of the well-known Rényi-Ulam game. Two playersthe Questioner and the Responder -play against each other. The Responder thinks of a number from the set {1, . . . , } and the Questioner has to find this number. To do this, he can ask if the sought number is an element of a subset of {1, . . . , } with at most elements. The Responder answers with YES or NO immediately, but during the game he may lie at most ℓ times. The minimal number of queries needed for the Questioner to find the unknown element in the worst case is denoted by ℓ ( ). First, we develop a highly effective tool, which we call Convexity Lemma. Using this, we give a general lower bound of ℓ ( ) with an error at most 2ℓ + 1, and we also give its exact value when is sufficiently large with respect to . With this, we manage to improve and generalize the results obtained by Meng, Lin and Yang in a 2013 paper about the case ℓ = 1.

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