Inclusion criteria: - Histologically confirmed advanced solid tumor for which there are no effective standard therapy options - Willing to provide tumor tissue for p53 wild type gene analysis Eastern Cooperative Oncology Group (ECOG) performance status of ≤1 - Adequate organ function - Female participants and male participants and their partners who are of childbearing potential must agree to abstain from sexual intercourse or to use an acceptable method of contraception during the study and for 90 days following the last dose of study therapy - At least one measurable lesion - In Part 2, participants with liposarcoma must have a confirmed well-differentiated or de-differentiated histology Exclusion criteria: - Known treated or untreated leptomeningeal metastases, or metastatic central nervous system disease - History of recent myocardial infarction (within the past year); or with unstable or uncontrolled angina, New York Heart Association (NYHA) Class III or IV congestive heart failure, uncontrolled hypertension, clinically significant cardiac dysrhythmia or clinically significant electrocardiogram (ECG) abnormality - Uncontrolled active infection on optimal systemic treatment - Clinically significant hepatitis or hepatitis C antibody positive, hepatitis B surface antigen positive, or human immunodeficiency virus (HIV) seropositive - Persistent, unresolved common terminology criteria for adverse events (CTCAE v4.0) ≥Grade 2 drug-related toxicity associated with previous treatment except for alopecia - Radiation therapy or other loco-regional therapy within 2 weeks prior to study - Use of moderate and strong Cytochrome P450 inhibitors or inducers within 1 week prior to study - Chemotherapy or any investigational drug(s) within 4 weeks prior to study - Known hypersensitivity to MK-8242 or its components - Nursing, pregnant, or intention to become pregnant during the study - Initiating bisphosphonate therapy or adjusting the bisphosphonate dose or regimen within 30 days of Cycle 1 Day 1