Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

Can you replace the X (both small and big x) with the numbers between 1 to 19 such that all the rows of 3 numbers between X (big x) sum to 23?

John is a strange liar.

He lies on six days of the week, but on the seventh day, he always tells the truth.

He made the following statements on three successive days:

Day 1: "I lie on Monday and Tuesday."
Day 2: "Today, it"s Thursday, Saturday, or Sunday."
Day 3: "I lie on Wednesday and Friday."

On which day does John tell the truth?

How do you go from 98 to 720 using just one letter?

What is the last thing you take off before bed?

Which English verb becomes past tense just by rearranging the letters?

If nine thousand, nine hundred nine dollars is written as $9,909,
how should twelve thousand, twelve hundred twelve dollars be written?

Eight of us go fourth, not back, to protect our king from an attack. What are we?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

There are two words one resembles the "state of rest" and the other is related to "writing/reading material".

Can you name these two words which also sound similar?