During a recent expedition, three intrepid adventurers were left stranded in the middle of the desert with only a crate full of apples.
During the night, Alan woke up and decided to hide his share of the apples and hid a third, then promptly fell asleep again.
Brian woke up shortly after and also decided to hide a third of the remaining apples and he also dozed back to sleep.
Finally, Charlie woke up and seeing the others were asleep, took a third of what was left.
Of course none of the adventurers knew of the other's antics, so, in the morning, they shared the remaining apples, each receiving sixteen. How many apples were in the crate originally?
[Ref: ZRZE] © Kevin Stone
Hint: How many apples were left after Charlie had taken some?
Alan hid 54, leaving 108. Brain hid 36, leaving 72. Charlie hid 24, leaving 48. 48 apples were then available to share in the morning.
To work these numbers out, we start at the end and work backwards.
At the end there were 16 apples each, therefore there were 48 apples.
Charlie removed 1÷3 leaving 48, so there must have been 72 apples before he did this.
Brian removed 1÷3 leaving 72, so there must have been 108 apples before he did this.
Alan removed 1÷3 leaving 108, so there must have been 162 apples before he did this. QED.
I started out on the journey from the badlands with a full tank of fuel, 12 gallons exactly.
However, the moment I started out, the fuel tank sprung a leak. I travelled at 50 mph until I ran out of fuel exactly 4 hours later.
I know that the car does 25 miles for each gallon.
How much fuel had I lost through the hole?
[Ref: ZVZE] © Kevin Stone
Hint: How many miles did I travel?
Answer: I had lost 4 gallons.
Since I travelled at 50 mph for 4 hours = 200 miles, I used 8 gallons for my journey.
At the local BrainBashers Sunday School meeting, the teacher brought in some puppies.
There were 20 more children than puppies.
In the corner of the room, within the ant's nest, the number of ants was 10 times the number of children.
In total, including the teacher, the children, the puppies and the ants, there were 1440 legs in the room.
How many children attended?
[Ref: ZIKX] © Kevin Stone
Hint: Work out the total number of legs.
23 children (46 legs).
With 230 ants (1380 legs), 3 puppies (12 legs) and 1 teacher (2 legs).
If we call the number of puppies P, then there were (P + 20) children and 10 x (P + 20) ants, and a single teacher. If we now count the legs, we get:
Puppies : P x 4 = 4P
Children: (P + 20) x 2 = 2P + 40
Ants : 10 x (P + 20) x 6 = 60P + 1200
Teacher : 2 = 2
66P + 1242
66P + 1242 = 1440
66P = 198
P = 3
So there were 3 puppies, hence 23 children. QED.
Fred can eat 27 chocolates in a hour, Alice can eat 2 chocolates in 10 minutes, and Kelly can eat 7 chocolates in 20 minutes.
How long will it take them to share and eat a large box of 120 chocolates whilst watching a movie?
[Ref: ZGBB] © Kevin Stone
Hint: In total how many chocolates are eaten each hour.
Answer: 2 hours.
In one hour, Fred eats 27 chocolates, Alice eats 12, and Kelly eats 21. A total of 60 chocolates. Therefore 120 chocolates would take 120 ÷ 60 = 2 hours. QED.
I want to travel 1,000 miles on an adult tricycle and I have two spare tyres.
However, I want to use all five tyres equally and have an equal mileage on each of the five tyres by the end of the trip.
Of course I can only use three tyres at a time, so I will have to change tyres during the trip.
At the end of the trip how many miles will each tyre have been used?
Hint: How many tyre miles have been travelled?
Answer: 600 miles.
A total of 1,000 miles have been travelled and at any one time, three tyres are travelling. Therefore 3,000 tyre miles have been travelled, which is shared equally by the 5 tyres. QED.