Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

A word I know,
Six letters contain,
Subtract just one,
And twelve is what remains.

A car meter reading shows 72927 miles a palindromic number.
what is the minimum number of miles you would need to travel to see another palindromic number on the car meter reading?

John gave half of the apples he had plus one more to Jacob. He gave half of the remaining ones plus one more to James. Now, John was left with just one apple.

Can you find out how many did he have in the beginning?

A man has to get a fox, a chicken, and a sack of corn across a river.

He has a rowboat, and it can only carry him and one other thing.
If the fox and the chicken are left together, the fox will eat the chicken.
If the chicken and the corn are left together, the chicken will eat the corn.

How does the man do it?

You have a roll of cloth 1km long. You have a machine which cuts this roll into pieces of 10-meter-long cloth.

How long would it take for the machine to cut the roll if each cut took 4 secs?

In a supermarket, there is an intelligent glass pane before a refrigerating unit. This glass pane allows cherries and apples through it but does not allow grapes and Orange to pass through it.

Can you identify the rule that the glass pane is following?

Why 1729 is a magic number? Answer Logically.

I have branches, but no fruit, trunk or leaves. What am I?

Railroad Crossing, look out for the cars. Can you spell that, without any R's ?