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

Three cars are driving on a track that forms a perfect circle and is wide enough that multiple cars can pass anytime. The car that is leading in the race right now is driving at 55 MPH and the car that is trailing at the last is going at 45 MPH. The car that is in the middle is somewhere between these two speeds.
Right now, you can assume that there is a distance of x miles between the leading car and the middle car and x miles between the middle car and the last car and also, x is not equal to 0 or 1.
The cars maintain their speed till the leading car catches up with the last car and then every car stops. In this scenario, do you think of any point when the distance between any two pairs will again be x miles i.e. the pairs will be x distance apart at the same time ?

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who Am I?

Lifeless eyes on my smiling face and watch your child's sleeping place. In their dreams they hold me tight. What am I?

Place the numbers from 1 to 9 in the circles in a manner that each side of the triangle sums up to 17.

What is harder to catch the faster you run?

Can you think of a smallest +ve number such that if we shuffle the digits of the number, the new number becomes double the original number?

On the occasion of Diwali, online seller companies in India are offering a big discount on Iphone14 as below.

: Flipkart offers a Flat 65% discount
: Amazon offers a 10% discount over and over again.
: Shopclues offers RS.45,000 off.

If the original cost of the iPhone is Rs.70,000 Which is the best offer for you?

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?

There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?