The Chocolate Bar Challenge
James and his friends are sharing a large chocolate bar. If James divides it equally among 4 friends, there are 3 pieces left. However, if he divides it equally among 7 friends, there is only 1 piece left. What is the smallest possible number of pieces in the chocolate bar?
James has a chocolate bar with N pieces.
ReplyDeleteWhen he divides it among 4 friends, there are 3 pieces left.
When he divides it among 7 friends, there is 1 piece left.
We need to find the smallest possible number of pieces in the chocolate bar.
Step 1: Write the Conditions as Equations
Since dividing by 4 leaves a remainder of 3, we can say:
N = a multiple of 4 + 3 → (e.g., 3, 7, 11, 15, 19, 23, …)
Since dividing by 7 leaves a remainder of 1, we can say:
N = a multiple of 7 + 1 → (e.g., 1, 8, 15, 22, 29, 36, …)
Step 2: Find the Smallest Common Number
The smallest number that appears in both lists is 15.
Final Answer:
The chocolate bar has at least 15 pieces. ✅