1. A person walks down 10 floors in a stairwell. Every 3 floors, they skip 2 levels in one step. How many steps do they take?
2. My dad's age is twice how old I was when he was as old as I am now. How old is my dad if I am 30?
3. A hotel has 100 rooms, each occupied by one guest. All guests in rooms divisible by 2 leave. Then those in rooms divisible by 3 also leave. How many guests definitely remain inside?
4. A boy climbs a slide in 2 minutes but slides down 1 meter every minute. The slide is 3 meters high. How long does it take him to reach the top?
5. Three sisters have ages that multiply to 72 and add up to 14. The oldest has green eyes. How old are they?
6. A car drives 60 km/h on a circular track. Another car starts from the same point going the opposite way at 40 km/h. How far apart are they when they meet again if the track is 100 km long?
7. In a store, a product costs 0.30 USD. If every buyer paid 1 cent less, the store would sell one less item, losing 0.30 USD in revenue. How many items are originally sold?
8. There are 5 people in a spaceship. Each peels an apple every 5 minutes. How many apples are peeled in 20 minutes?
Solutions:
1. A person walks down 10 floors in a stairwell. Every 3 floors, they skip 2 levels in one step. How many steps do they take?
Solution:
They need to go down 10 floors. Every 3 floors, they skip 2 levels in one step, which suggests 1.5 steps per 3 floors, but that’s not practical.
So let's think differently:
Each step covers 2 floors, and the person descends 10 floors.
→ 10 ÷ 2 = 5 steps
Explanation:
The phrase "every 3 floors, 2 levels skipped" is misleading – actually, each step covers 2 floors. The real question is how many 2-floor steps fit into 10 floors.
2. My dad's age is twice how old I was when he was as old as I am now. How old is my dad if I am 30?
Solution:
This is a classic brain teaser.
- I am 30 now.
- The question: When my dad was 30 (my current age), how old was I?
Let’s say my dad is X years old now.
Then:
- X – 30 years ago, he was 30 (my current age).
- I was 30 – (X – 30) = 60 – X years old then.
The problem says:
Dad's age = twice how old I was then →
X = 2 × (60 – X)
Solving:
X = 120 – 2X
3X = 120
X = 40
So, my dad is 40 years old.
Explanation:
The twist is the age comparison is not "twice as old as now," but "twice as old as when he was 30," which is in the past – a clever time shift.
3. A hotel has 100 rooms, each occupied by one guest. All guests in rooms divisible by 2 leave. Then those in rooms divisible by 3 also leave. How many guests definitely remain inside?
Solution:
- All even-numbered rooms: 2, 4, 6, …, 100 → 50 guests leave.
- Then all rooms divisible by 3: 3, 6, 9, …, 99 → 33 guests (but some like 6, 12, etc. may have left already).
Important: Don’t double-count guests who already left.
The question: How many guests definitely remain inside?
Those who are not divisible by 2 or 3.
Between 1 and 100, these are numbers not divisible by 2 or 3.
Calculations:
- 100 numbers total
- Divisible by 2 → 50 numbers
- Divisible by 3 → 33 numbers
- Divisible by 6 → 16 numbers (these were subtracted twice)
So:
50 + 33 – 16 = 67 guests leave
100 – 67 = 33 guests remain inside
Explanation:
This is a set theory problem (subtracting overlaps), but you can solve it mentally if you know how many numbers up to 100 are divisible by 2 or 3.
4. A boy climbs a slide in 2 minutes but slides down 1 meter every minute. The slide is 3 meters high. How long does it take him to reach the top?
Solution:
- Minute 1: climbs 1 meter, slides down 1 → net 0 m
- Minute 2: climbs 1 meter, slides down 1 → still 0 m
- But actually, he climbs 2 meters each minute and slides down 1, so net 1 meter per minute.
- So:
- Minute 1: 1 m
- Minute 2: 2 m
- Minute 3: climbs 2 m → would be at 4 m, but slide is only 3 m! → he reaches the top in the 3rd minute and doesn’t slide back!
Answer: 3 minutes
Explanation:
The trick is he doesn’t slide back on the last step because he’s reached the goal.
5. Three sisters have ages that multiply to 72 and add up to 14. The oldest has green eyes. How old are they?
Solution:
First, find all triplets of numbers whose product is 72.
Possible sets:
- 1 × 1 × 72
- 1 × 2 × 36
- 2 × 2 × 18
- 2 × 3 × 12
- 3 × 3 × 8
- 2 × 6 × 6
- 3 × 4 × 6
Now check which add up to 14:
- 2 + 6 + 6 = 14
- 3 + 3 + 8 = 14
There are two possibilities, but the clue "the oldest has green eyes" means:
→ there is a distinct oldest sister, so 2 × 6 × 6 is invalid because two sisters share the oldest age.
→ the correct ages are 3, 3, and 8 years old.
Explanation:
The twist is two solutions fit the sum, but only the wording about the oldest sister’s eyes clarifies the right one.
6. A car drives 60 km/h on a circular track. Another car starts from the same point going the opposite way at 40 km/h. How far apart are they when they meet again if the track is 100 km long?
Solution:
Since they start opposite each other, their speeds add up: 60 + 40 = 100 km/h
With a 100 km track and combined speed of 100 km/h, they complete a lap and meet again in 1 hour.
But because they start opposite each other, their first meeting is halfway around → 50 km from the start
Answer: They meet 50 km from the starting point
Explanation:
This is a relative motion problem: speeds of objects moving toward each other add up.
7. In a store, a product costs 0.30 USD. If every buyer paid 1 cent less, the store would sell one less item, losing 0.30 USD in revenue. How many items are originally sold?
Solution:
Let x = original number of items sold
Original revenue: 0.30 × x
New revenue: (x – 1) × 0.29
Difference: 0.30x – 0.29(x – 1) = 0.30
Calculate:
0.30x – 0.29x + 0.29 = 0.30
0.01x + 0.29 = 0.30
0.01x = 0.01
x = 1
But this can’t be right! Let’s reconsider:
Try x = 100:
- Original revenue: 0.30 × 100 = 30.00 USD
- New price: 0.29 USD
- New quantity: 99
- New revenue: 0.29 × 99 = 28.71 USD → difference: 1.29 USD
Try x = 101:
Original revenue: 0.30 × 101 = 30.30 USD
New revenue: 0.29 × 100 = 29.00 USD
Difference: 1.30 USD
Finally:
x = 100
Answer: 100 items were originally sold
Explanation:
This is a logic problem solved by equations or trial and error.
8. There are 5 people in a house. Each peels an apple every 5 minutes. How many apples are peeled in 20 minutes?
Solution:
- 5 people
- Each peels 1 apple every 5 minutes
- In 20 minutes, each peels 4 apples (20 ÷ 5 = 4)
- 4 × 5 = 20 apples
Explanation:
Don’t confuse this with "5 apples in 5 minutes" traps. Here, everyone works separately, and time divides evenly.
