Who is asking: Parent
Level: Secondary
Question:
Today is Monday, 1 October 2001. What day of the week will be 29833 days
from today?
Hi Pauline,
Suppose that you were to write a list if all 9833 powers of 2 and the corresponding day of the week. The list would start
| n | 2n | day of the week |
|---|---|---|
| 1 | 2 | Wednesday |
| 2 | 4 | Friday |
| 3 | 8 | Tuesday |
| 4 | 16 | Wednesday |
| 5 | 32 | Friday |
The pattern will repeat, Wednesday, Friday, Tuesday, Wednesday, Friday, Tuesday,...
Day 16 is on a Wednesday since 16 = 2 
7
+ 2 (2 weeks and 2 days after October 1)
Day 32 is on a Friday since 32 = 4 7
+ 4 (4 weeks and 4 days after October 1)
...
Now imagine that the list above is extended to 9833 rows. How many times does this cycle of three days repeat? How many rows are in the table after that? What day of the week is the last row of the table?
Penny