Challenge 3 - Desert island
Challenge 3 is all about calculating numbers.
Maths teacher Chris Smith and pupils from Grange Academy are here to explain.
The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.
Mr Smith: This problem is all about numbers.
In the final week of reality TV series "Stranded", the remaining four contestants on a desert island have nothing to eat but a pile of coconuts.
One coconut is stolen by a passing monkey, and the contestants share the rest out equally among themselves.
All the contestants ration their coconuts carefully, each eating one for breakfast, one for lunch and one for dinner on each of the four remaining days of the competition. Each is left with one spare coconut.
What is the smallest number of coconuts that there could have been in the original pile?
Pupil 1: You can work this out with simple addition or multiplication.
Pupil 2: Try working out the number of coconuts there were per person.
Pupil 3: Don’t forget the spare coconuts.
Give it a go!
So here's the challenge:
This problem is all about numbers.
Four contestants on a desert island share a pile of coconuts, but one coconut is stolen by a passing monkey, and the contestants share the rest out equally among themselves.
All the contestants ration their coconuts, eating one for breakfast, one for lunch and one for dinner on each of the four remaining days of the competition. Each is left with one spare coconut.
What is the number of coconuts that there could have been in the original pile?
Need a hint?
- You can work this out with simple addition or multiplication.
- Try working out the the number of coconuts there were per person.
- Don’t forget the spare coconuts.
Solution
Worked out the answer? Here's how you can do it.
Mr Smith: Did you work out the number of coconuts there were on the desert island?
Let’s look at how we got our answer.
You might have used a bit of addition and multiplication to find the solution
Or, we can put the information that we have into an equation.
Let’s call the total number of coconuts in the pile n. After the monkey takes one it’s n-1
Each contestant receives n-1 ÷ 4
But we know each contestant eats 3 a day over 4 days, with one left over, which is 13 coconuts.
So, n-1 ÷ 4 = 13
Let’s solve this.
Multiply by 4 to get
n-1 = 52
Add 1 to both sides to find n = 53
There were 53 coconuts in the original pile.
Great job if you survived this one.
Step 1
One way to solve this challenge is to put the information that we have into an equation.
Let’s call the total number of coconuts in the pile n.
After the monkey takes one it’s n-1
Step 2
Each of the four contestants receives an equal share so this becomes
\(\frac{n-1}{4}\)
Step 3
But we know each contestant eats 3 coconuts a day in the remaining 4 days, with one left over.
So \(\frac{n-1}{4}=3\times1\times4+1\)
Step 4
This is gives us 13 coconuts per contestant.
So, \(\frac{n-1}{4}=13\)
Step 5
Let’s solve this. Multiply by 4 to get \(n-1= 52\)
Add 1 to both sides to find \(n = 53\)
There were 53 coconuts in the original pile.
Alternative solution
Another way to solve this is to use addition and multiplication to find the solution.
Step 1
Add up the coconuts each contestant eats each day:
1 for breakfast + 1 for lunch + 1 for dinner = 3
Step 2
Multiply by the number of days:
3 coconuts × 4 days = 12
Step 3
Add on the spare coconut:
12 + 1 = 13
Step 4
Multiply by the number of contestants:
13 × 4 = 52
Step 5
Add back the coconut stolen by the monkey:
52 + 1 = 53 coconuts in total.
Maths problem solving. collection
Try out Maths Week Scotland challenges from previous years.
Maths Week Scotland. External Link
Find more maths challenges and activities at the Maths Week Scotland website.
More on Maths Week Scotland 2025
Find out more by working through a topic
