# Thread: if today is Tuesday, what day will it be in 129 days?

1. ## if today is Tuesday, what day will it be in 129 days?

Sun=0, Mon=1,....

$\displaystyle 2+129\equiv x \ \mbox{(mod 7)}\rightarrow 131\equiv x \ \mbox{(mod 7)}$

Here is what I did, and I obtained the correct answer; however, I think this should have been done another way.

$\displaystyle 131-\left \lfloor \frac{131}{7} \right \rfloor*7=5$

$\displaystyle 131\equiv 5 \ \mbox{(mod 7)}$

In 129 days, it will be Friday.

2. Every 7 days, you get back to Tuesday.

Since $\displaystyle 129 = 18\cdot 7 + 3$ that means that it will be $\displaystyle 3$ days after Tuesday.

So the day you'll be on is Friday.

3. Originally Posted by Prove It
Every 7 days, you get back to Tuesday.

Since $\displaystyle 129 = 18\cdot 7 + 3$ that means that it will be $\displaystyle 3$ days after Tuesday.

So the day you'll be on is Friday.
To explain Prove It's method a bit further, you're seeking $\displaystyle r$ such that $\displaystyle 0\leq r <7$ and $\displaystyle 129=7q+r$.

$\displaystyle q,r$ can be found through the division algorithm.