I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

Katniss and Peeta are liars. They both lie on some specific days.

Katniss lies on Fridays, Saturdays and Sundays. She speaks the truth on all other days.

Peeta lies on Tuesdays, Wednesdays and Thursdays. He speaks the truth on all other days.

Can you tell that one day of the week when both of them will say "Tomorrow, I will lie."?

I’m tall when I’m young, and I’m short when I’m old. What am I?

Find the next number in the sequence

1, 2, 6, 21, 88, __?

If we change the South-East direction into North and North-East into West and all others similarly.
Can you find out which direction will be in the place of South-West direction?

Can you decipher the following common phrase?

T M C
A U O
H S M
W T E

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

Replace the (?) with the correct mathematical signs to make the expression equal to 59.

18 ? 12 ? 4 ? 5 = 59

John enters a small room. The Door Closes.
When the door opens, John is in a larger room.

Explain?

Can you calculate the probability of getting a sum of six when a dice is thrown twice?