Trick of Mind

What number(s) come next in this sequence?
61, 52, 63, 94, 46, ….

What is the 5-digit number in which the sum of the first two digits is one smaller than the third, the third is double the fourth, the fourth is double the last, the third is the product of the fourth and fifth, the second is five more than the first, and the first is one-eighth [...]

Two x Two = Three
Can you make this work?

Eketahuna is having a party. The party was to be held in his private mansion in the city of Puzzlaria. The city, conveniently, is laid out in a perfect grid. Every house’s address is composed of two positive numbers, indicating its relative position to the Town-hall in the southwest corner. For example, House 3-8 [...]

You have a single six sided die with one integer on each side. The integers are random positive numbers and do not repeat.
When the die is rolled, it is placed against a wall, which means 4 sides are visible, the front, the top and the two sides, and the bottom and back are hidden from [...]

Two skaters start skating at the same time from the same point.
Eketahuna skates at 5m/s, and prescribes an exact square, 25 meters by 25 meters. He starts travelling north.
Chris starts skating south at 6m/s, prescribing a rectangle with sides 40 meters by 25 meters.
The two skaters skating in rectangles have one 25m side (the [...]

In a friends extensive library he has 5 books. As you can see, what we have here is a reader, which has gotten him into a lot of trouble in the deep south of a one-time English colony.
Each of his 5 volumes are 400 pages long. They are meticulously shelved according to his own Dewey-decimal [...]

Hi guys, long time no see.
Here i give two infinite series:
1) What are all the possible values of the following series?
1-1+1-1+1-1+1-1+1-1+1……to infinity
2) What are all the possible values of ‘x’ for which the following series converges.
((((((x-2)²-2)²-2)²-2)²-2)²-2)²……..

What is the smallest integer that ends with a 3 and that when that 3 is moved from the end to the beginning, makes the number 3 times as large.
i.e. I want something like 312 = 3*123 (which obviously doesn’t work).