Three brothers Jacob, John, and James live in Mexico City. The product of the ages of these brothers is 175. Jacob and John are twins. How old is James?

A patient was diagnosed with some ailment. He was given five different tablets to take at night at an interval of 15 minutes.

How long will it take the patient to consume all the five tablets?

It can be easily calculated that the digits 0 to 9 can be arranged into 3628800 distinct ten-digit numbers.

But do you know how many of these numbers are prime?

Find the missing number in the series below

13 -21 34 -55 ? -144

There are three light switches outside a room. One of the switches is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

Name a key which is hardest to turn.

John is 45 years older than his son Jacob. If you find similarities between their ages, both of their ages contain prime numbers as the digits. Also, John's age is the reverse of Jacob's age.

Can you find their ages?

One night, a woman receives a call from the police. They tell her that her husband was murdered and that she should come to the crime scene as soon as possible. The woman drops the phone, shocked, and drives 20 minutes to the crime scene. As soon as she reaches the crime scene, the police arrest her and she is convicted of murder. How do the police know she committed the crime?