Reasoning
Take the numbers in pairs, square the first, and reverse the digits.
1 1 (1 x 1 = 1, reversed is 1)
2 4 (2 x 2 = 4, reversed is 4)
3 9 (3 x 3 = 9, reversed is 9)
4 61 (4 x 4 = 16, reversed is 61)
5 52 (5 x 5 = 25, reversed is 52)
6 63 (6 x 6 = 36, reversed is 63)
7 94 (7 x 7 = 49, reversed is 94)
so we require:
8 46 (8 x 8 = 64, reversed is 46)
A million grains of sand is a heap. If we remove one grain of sand from this heap, we will still have a heap.
We can now keep repeating (2) until we only have a single grain of sand remaining.
Is this a heap? Clearly not. But what went wrong with our thinking?
This is called the Sorites paradox (soros being Greek for "heap") and is a classic paradox that has no real answer.
Both (1) and (2) are true, and we can indeed keep removing one grain of sand until we have a single grain remaining. If we remove one more grain, we're left with nothing, is this still a heap?
