Task: Abstract reasoning — arithmetic reasoning
Question: The ChronoCorp "Temporal Singularity" Challenge
Following the "success" of Project Chimera, ChronoCorp has initiated "Project Singularity." Its timeline is governed by quantum mechanics, corporate bureaucracy, and a concerning disregard for the linear progression of time. Your task is to calculate its completion.
Timeline & Constraints
Phase A (Initiation): The project was initiated in Tokyo, Japan (JST, UTC+9) at 1:00 PM on Monday, February 26, 2024 (a leap year). This phase had a fixed duration of exactly 100 hours.
Phase B (Development): This phase consists of 10 "work cycles" (a work cycle is 72 hours). It begins 48 hours after Phase A is complete. Crucially, exactly halfway through its duration, Phase B is paused for a mandatory 30-hour "Quantum Entanglement Review" before work can resume.
Phase D (Security Audit): The audit (Phase D) begins exactly 3 days after Phase A concludes and has a fixed duration of 150 hours.
Phase C (Integration & Resource Conflict):
The integration work for Phase C is performed by a team in Bangalore, India (IST, UTC+5:30) and takes 200 hours to complete.
Both Phase C and Phase D require exclusive use of the company's lone "Chronos Server." Phase D has priority. Therefore, Phase C can only begin after both Phase B and Phase D are fully complete.
The Bangalore team only works between 8:00 AM and 8:00 PM IST. If the prerequisite tasks finish outside this window, Phase C cannot begin until the next available 8:00 AM IST start time.
Probabilistic Projections & Final Approval:
There is a 20% probability that the Chronos Server will require a 48-hour automated maintenance period immediately after Phase D finishes.
If and only if this server maintenance occurs, there is a subsequent 50% probability that the integration work (Phase C) will take an additional 24 hours to complete due to residual server cache issues.
Final approval is given by the CTO in San Francisco, USA. The project spans the Daylight Saving Time change in the US (on March 10, 2024), so be mindful of the shift from PST (UTC-8) to PDT (UTC-7).
The CTO can only grant approval during local business hours (Monday-Friday, 9:00 AM to 5:00 PM). If all work is completed outside this window, approval must wait for the next available time slot.
Your Task
What is the expected completion time of all project work in UTC? This must be a single timestamp, representing the probabilistically weighted average of all possible outcomes. Show your calculations for each potential timeline.
Considering only the most probable timeline (the one with no probabilistic delays), what is the exact final date and local time in San Francisco that the CTO actually gives her approval?
Solution: A correct solution must compute all phase times exactly using the stated offsets and time zones, and it must keep the scenarios internally consistent. 
Key corrections:
Phase A completes 2024-03-01 08:00 UTC (100h after 2024-02-26 04:00 UTC);
Phase D completes 2024-03-10 14:00 UTC (3 days + 150h after Phase A = 222h);
Phase B completes 2024-04-02 08:00 UTC (48h + 10×72h = 768h = 32 days after Phase A), not 2024-04-03.
If Phase C starts immediately after Phase B, then with 0.5h on day 1, 16×12h on the next 16 days, and 7.5h on the final day (total 200h), Phase C completes 2024-04-19 10:00 UTC and the next Monday approval is 2024-04-22 16:00 UTC; with an added 24h of work, completion shifts to 2024-04-23 10:00 UTC and approval is 2024-04-23 16:00 UTC. 

A common incorrect behavior is arithmetic slips on hour-to-day conversion, drifting dates by one day, or mixing UTC/IST/PDT conversions.