self Maths Puzzle

While enjoying a giddy ride at the carousel Sammy propounded a puzzle which reflects much credit to his mental abilities.

"One third of the number of kids riding ahead of me, added to three-quarter of those riding behind me gives the correct number of children on this Merry-Go-Round" is the way he puts it; but it will puzzle you quite a little to tell just how many riders there were at this whirling circus.

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self Other Question

What are the maximum number of grape vines that can be planted, not closer than nine feet apart, in a square plot containing one-sixteenth of an acre?

(Note: each side of this square plot would be 52 feet 2 inches)
Here is a famous prize problem that Sam Loyd issued in 1882, offering $1000 as a prize for the best answer showing how to arrange the seven figures and the eight "dots" .4.5.6.7.8.9.0. which would add up to 82.

Out of several million answers, only two were found to be correct.