Sharing sweets
Maria and Lucy spun a coin 30 times, and gave each other sweets depending on the outcome of the spin. How many times was tails spun?
Age
11 to 14
Challenge level
Problem
Maria and Lucy spun a coin $30$ times.
Whenever the coin showed heads, Maria gave $2$ sweets to Lucy.
Whenever the coin showed tails, Lucy gave $3$ sweets to Maria.
After all $30$ spins, Maria and Lucy both had the same number of sweets that they started with. How many times did the coin show tails?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 12 tails
Image
Back to where they started after 3 heads and 2 tails (5 spins)
Repeat 6 times (30 spins)
12 tails
Repeat 6 times (30 spins)
12 tails