You are going to meet your school friends after four years. You are very excited about it. You have planned to gift everyone a chocolate.
On the day of get-together you meet everyone and feel happy to share the sweet old memories. Everyone is glad to meet old pals, there are hugs all around, cheers and laughter and smile. Suddenly, you see that girl you had a crush on. All those nostalgic feelings about your shyness and fantasies are revived. You come back to your senses and you decide that you will give most of the chocolates to her and distribute rest chocolates as supper.
As the dinner is about to start in about half an hour, you have to start the job of cutting chocolates into smaller pieces quickly.
A chocolate is a cuboid of size $10$cm x $4$cm x $2$cm .
You go to your room of the hotel and cut chocolates as following:
- You open the wrappers of half the chocolates(as the half would be used to impress your 'first love').
- You put some pieces of chocolate together on the table and cut them with a knife at one time. You can cut as many pieces of chocolate as you want to give to others.
- Then you think that it'd be better to get unit-size pieces(cubes of size $1$×$1$×$1$) and then give the pieces accordingly.
Since you are really short of time, you want to calculate the minimum number of cuts required for the above said method. The question is:
What should be your strategy for minimum cuts of chocolates? (and what is minimum no. of cuts for this)
- The exact number of friends who will come to party is not known. Assume it to be $S$ (where $S \ge 10$) and you have bought $S$ chocolates...
- Your cutting speed is constant throughout.
- Knife is long enough to cut in one swing ( or imagine you have a katana)!
- Half of the chocolates will be gifted to that special girl ;)