1. ## math puzzles

1. 13 balls are given of which only 1 is different. We do not know whether the given is heavier or lighter. How will you determine in just three measurments, the odd ball?

2.If the day after tomorrow was yesterday, then Sunday would be what today was. If the day before yesterday was the day after tomorrow, then what is today?

3. Find the probability that in a gathering of 50 people,two persons birthday fall in the same day.

4. How many balls can be placed around one ball of the same size so that the later touches each of the former one.

3. Hello, mathwizard!

2. If the day after tomorrow was yesterday, then today would be Sunday.
If the day before yesterday was the day after tomorrow, then what is today?
"If the day after tomorrow is yesterday, then today is Sunday."

. . . . . $\displaystyle _{\downarrow} \qquad \leftarrow \qquad \leftarrow \qquad \leftarrow \qquad\leftarrow\qquad \leftarrow \qquad _{\uparrow}$

. . $\displaystyle \boxed{\text{yesterday}} \quad \boxed{\text{today}} \quad \boxed{\text{tomorrow}} \quad \boxed{\text{day after tomorrow}}$
. . . . . . . . . . $\displaystyle ^{\text{Sunday}}$

We can see that everything is "set back" three days.
To restore it, everything is "set ahead" three days.

. . Hence, today is: .$\displaystyle \text{Sunday}+3\quad\rightarrow\quad\boxed{\text{ Wednesday}}$

"If the day before yesterday is the day after tomorrow..."

. . . . . . . . . . $\displaystyle _{\uparrow}\qquad \rightarrow \qquad\rightarrow\qquad\rightarrow\qquad\rightarro w \qquad\rightarrow \qquad\rightarrow\qquad\rightarrow\qquad_{\downarr ow}$
. . $\displaystyle \boxed{\text{day before yesterday}} \quad \boxed{\text{yesterday}} \quad \boxed{\text{today}} \quad \boxed{\text{tomorrow}} \quad \boxed{\text{day after tomrrow}}$
. . . . . . . . . . . . . . . . . . . . . . . .$\displaystyle ^{\text{Wednesday}}$

We see that everything is "moved ahead" four days.

Therefore, today is: .$\displaystyle \text{Wednesday}+4\quad\rightarrow\quad\boxed{\tex t{Sunday}}$

4. Originally Posted by Soroban
Hello, mathwizard!

"If the day after tomorrow is yesterday, then today is Sunday."

. . . . . $\displaystyle _{\downarrow} \qquad \leftarrow \qquad \leftarrow \qquad \leftarrow \qquad\leftarrow\qquad \leftarrow \qquad _{\uparrow}$

. . $\displaystyle \boxed{\text{yesterday}} \quad \boxed{\text{today}} \quad \boxed{\text{tomorrow}} \quad \boxed{\text{day after tomorrow}}$
. . . . . . . . . . $\displaystyle ^{\text{Sunday}}$

We can see that everything is "set back" three days.
To restore it, everything is "set ahead" three days.

. . Hence, today is: .$\displaystyle \text{Sunday}+3\quad\rightarrow\quad\boxed{\text{ Wednesday}}$

"If the day before yesterday is the day after tomorrow..."

. . . . . . . . . . $\displaystyle _{\uparrow}\qquad \rightarrow \qquad\rightarrow\qquad\rightarrow\qquad\rightarro w \qquad\rightarrow \qquad\rightarrow\qquad\rightarrow\qquad_{\downarr ow}$
. . $\displaystyle \boxed{\text{day before yesterday}} \quad \boxed{\text{yesterday}} \quad \boxed{\text{today}} \quad \boxed{\text{tomorrow}} \quad \boxed{\text{day after tomrrow}}$
. . . . . . . . . . . . . . . . . . . . . . . .$\displaystyle ^{\text{Wednesday}}$

We see that everything is "moved ahead" four days.

Therefore, today is: .$\displaystyle \text{Wednesday}+4\quad\rightarrow\quad\boxed{\tex t{Sunday}}$

I would have thought it was thursday, not wednesday. since if today is sunday, yesterday would be saturday. which is the day after friday, which is "tomorrow" from thursday. oh well, i'm not good with puzzles i'm confusing myself