r/mathriddles

Here is a funny (I hope) home-made problem just for you guys :

Is there an ice cube such that, when it melts, the number of its connex components at a given instant t is 2 if t is rationnal, 1 otherwise ?

Precisions :

We suppose that this ice cube is a closed subset of R³.

We also suppose that the melting begins at t=0, and that after a delay t, all that remain of the ice cube A is every points x of A such that distance(x, surface A)>=t

Can you also find an ice cube in 2D having this property ?

AI couldn't solve it ! But your creativity can !

Given below is an incorrect equation.

Put an exact same whole number ( any number from 0 to 9) anywhere on BOTH sides ( LH and RH) to make the equation correct.

You must put the same number on both sides. You can use that number only once for each side. Cannot make any other changes like adding or taking out operators.

1 + 3 + 5 + 7 + 9 = 2 + 4 + 6 + 8 + 10

There are 3 possible answers I can think of.