Here's this week's collection. Answers & extensions can be found here. Why not discuss the problems on Twitter using #SundayAfternoonMaths. This Tuesday is Maths Jam, although I won't be there as it is also parents' evening at my school.

#### Arccos + Arcsin

What is the value of arccos(

*x*) + arcsin(*x*)?*i*^{ i}

What is the value of

*i*to the power of*i*?*x*^{xxxxx...}

If

*x*^{xxxxx...}[x to the power of (x to the power of (x to the power of (x to the power of (...)))) with an infinite number of*x*s] is equal to two, what is the value of*x*?#### 4 and 5 digit numbers

Adam chooses a 5-digit positive integer and deletes one of its digits to form a 4-digit integer. The sum of this 4-digit integer and the original 5-digit integer is 52713. What is the sum of the digits of the original 5-digit integer?

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