I have a square table that used to be perfectly stable, back when it had a foot at the end of each leg. Now the feet are missing from legs B, C, and D There's only one left at leg A.
The table measures 50 cm x 50 cm with legs 99.5 cm long. The foot is flat and attached by a swivel so that the end of leg A is a constant 0.5 cm from the ground. (In other words, the total length of leg A plus the foot is 100cm, 0.5 cm longer than each of the other three.)
The table can now rock back and forth with the foot of A and its opposite leg C in constant contact with the floor.
If B is also in contact with the floor, how far is D from the floor?
Note: consider the tips of the legs to be singular points at the corners of a square.
I am thinking of a 5 digit number that when tripled is a perfect square.
Also, when the 5 digit number is split, the first number is double the second one. What is the five digit number?
(Splitting the 5 digit number into two numbers means 12345 into 1 and 2345 or 123 and 45.)