Nguyệt keeps a bread dough in her fridge. She tends to it so that every day it doubles in size, and then every morning, she cuts off enough dough to make one loaf of bread for her breakfast.
Normally, Nguyệt’s dough is just the right size to grow that one loaf of dough every day. One Monday, Nguyệt went out for breakfast and didn’t cut off any dough, but the dough still doubled in size.
In the following days, Nguyệt followed the same routine as usual, cutting enough dough to make one loaf of bread, and leaving the rest to double in size.
By Saturday that week, Nguyệt realised she had too much dough, so she cut all the dough into loaves and baked them all.
How many loaves did Nguyệt bake on Saturday?
The first step to this puzzle is working out how much dough Nguyệt usually kept in her fridge. Remember that the growth was equal to the amount she was taking out of the dough each day!
The second part is following the pattern of growth. Don’t be surprised if Nguyệt ends up with a lot of bread!
Normally, the growth in the dough is matched by the amount that Nguyệt cuts off each morning. Since Nguyệt cuts off one loaf worth of dough each morning, it must grow one loaf worth each day. We know it’s doubling in size, so it must be one loaf in size after being cut.
On the first Monday, Nguyệt didn’t cut the dough, so it’s the size of 2 loaves at the start of the day.
On Tuesday morning, it has doubled to 4 loaves. Nguyệt cuts one off, leaving 3.
On Wednesday morning, it has doubled to 6 loaves. Nguyệt cuts one off, leaving 5.
On Thursday morning, it has doubled to 10 loaves. Nguyệt cuts one off, leaving 9.
On Friday morning, it has doubled to 18 loaves. Nguyệt cuts one off, leaving 17.
By Saturday morning, it has doubled to 34 loaves. That’s a lot of bread for Nguyệt to bake!