Daily Math Puzzle: 2026-09-30
Sharpen your mathematical thinking with fresh puzzles delivered daily.
🧩 New Puzzle Every Day — Free
2026-09-30
At the "Wheel of Fortune" stall in an amusement park, there are 10 opaque boxes. You're told that 3 of these boxes contain a "Lucky Wheel" (which has an 80% chance of landing on a prize sector) and the remaining 7 boxes contain a "Tricky Wheel" (which has only a 20% chance of landing on a prize sector). You randomly pick one box, take out the wheel, and give it a spin. The wheel lands on the prize sector. What is the probability that the wheel you spun was a Lucky Wheel?
🔥 Build your streak — solve daily in the app
Solution
12/19 — Let LW be the event of picking a Lucky Wheel, and TW be the event of picking a Tricky Wheel. Let P be the event of the wheel landing on a prize sector.
We are given the following probabilities:
1. P(LW) = 3/10 (The probability of picking a Lucky Wheel)
2. P(TW) = 7/10 (The probability of picking a Tricky Wheel)
3. P(P|LW) = 80% = 8/10 (The probability of getting a prize given it's a Lucky Wheel)
4. P(P|TW) = 20% = 2/10 (The probability of getting a prize given it's a Tricky Wheel)
We want to find P(LW|P), which is the probability that the wheel was a Lucky Wheel, given that it landed on a prize sector. We can use Bayes' Theorem for this:
P(LW|P) = [P(P|LW) * P(LW)] / P(P)
First, we need to calculate P(P), the total probability of landing on a prize sector, which can happen with either a Lucky Wheel or a Tricky Wheel:
P(P) = P(P|LW) * P(LW) + P(P|TW) * P(TW)
P(P) = (8/10 * 3/10) + (2/10 * 7/10)
P(P) = (24/100) + (14/100)
P(P) = 38/100
Now, substitute P(P) back into Bayes' Theorem:
P(LW|P) = (P(P|LW) * P(LW)) / P(P)
P(LW|P) = (8/10 * 3/10) / (38/100)
P(LW|P) = (24/100) / (38/100)
P(LW|P) = 24 / 38
P(LW|P) = 12 / 19
The correct answer is 12/19. Many might intuitively choose 4/5 (80%), assuming that since it landed on a prize, and Lucky Wheels have an 80% chance, it must be a Lucky Wheel. However, this ignores the initial low probability of picking a Lucky Wheel (3/10) and the fact that Tricky Wheels can also land on a prize, contributing to the observed event.
Never Miss a Daily Puzzle
Download TestPrepMagic and get push notifications for each day's puzzle. Build daily streaks and track your improvement.
Download Free AppRelated Puzzles
Math Puzzle: 2026-09-29
Detective Reese is on a crucial case, analyzing security footage from a suspect's secret lab. The lab has three security cameras: Alpha, Beta, and Gamma, all feeding into a single, fixed-capacity server. Camera Alpha records at a base rate 'R' GB/hour. Camera Beta records at twice Alpha's rate (2R GB/hour), and Camera Gamma records at thrice Alpha's rate (3R GB/hour).
Reese discovered the server was completely full. Examining the server logs, he pieced together the sequence of events:
1. Initially, only Camera Alpha was active, recording for a specific duration (let's call it 'T' hours).
2. Then, Camera Beta was activated, joining Alpha. Both Alpha and Beta recorded together for *half* the time Alpha had recorded alone (T/2 hours).
3. Finally, Camera Gamma was activated, joining Alpha and Beta. All three cameras recorded together until the server reached its full capacity.
Crucially, the server's logs also revealed a unique insight: the total amount of data recorded by Camera Alpha throughout *all phases* of its operation was exactly equal to the total amount of data recorded by Camera Beta throughout *all phases* of its operation.
What proportion of the server's total storage capacity was ultimately filled *only* by Camera Gamma's footage?
Math Puzzle: 2026-09-28
In the mystical realm of Eldoria, an ancient wizard offers you a chance to claim a legendary artifact. He presents a magical 'Orb of Fate' with three distinct faces: 'Success', 'Failure', and 'Neutral'. Each face has an equal probability of appearing when the orb is activated. You must activate the orb up to two times following these rules:
1. You activate the orb once.
2. If the first activation shows 'Success', you immediately win the artifact.
3. If the first activation shows 'Failure', you immediately lose the challenge and get nothing.
4. If the first activation shows 'Neutral', you must activate the orb a second time.
5. If the second activation shows 'Success', you win the artifact.
6. If the second activation shows 'Failure', you lose the challenge.
7. If the second activation shows 'Neutral', nothing happens; you neither win nor lose, ending the challenge inconclusively.
What is the probability that you win the legendary artifact?
Math Puzzle: 2026-09-27
The annual school field trip lunch menu had a tricky challenge! The number of 'PIES' and 'CAKE' available, when added together, magically spelled out 'FOOD' for the total items. Each letter in this equation represents a unique digit from 0-9, and no number starts with a zero. Can you decipher the unique digit represented by 'S'?