self Maths Puzzle

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)

Read Solution (Total 1)

This comes about by planting 6,5,6,5,6,5,6,5 trees in 8 layers with horizontal spacing 10.433 feet and layer distances 7.45 feet. Any 3 adjacent trees form a triangle with side lengths 10.433, 9.097, 9.097 feet.
12 years agoHelpfull: Yes(1) No(0)

self Other Question

t appears that an ingenious or eccentric teacher being desirous of bringing together a number of older pupils into a class he was forming, offered to give a prize each day to the side of boys or girls whose combined ages would prove to be the greatest.

Well, on the first day there was only one boy and one girl in attendance, and, as the boy's age was just twice that of the girl's, the first day's prize went to the boy.

The next day the girl brought her sister to school, and it was found that their combined ages were just twice that of the boy, so the two girls divided the prize.

When school opened the next day, however, the boy had recruited one of his brothers, and it was found that the combined ages of the two boys were exactly twice as much as the ages of the two girls, so the boys carried off the honors of that day and divided the prizes between them.

The battle waxed warm and on the fourth day the two girls appeared accompanied by their elder sister; so it was then the combined ages of the three girls against the two boys, and the girls won off course, once more bringing their ages up to just twice that of the boys'. The struggle went on until the class was filled up, but as our problem does not need to go further than this point, to tell the age of that first boy, provided that the last young lady joined the class on her twenty-first birthday. Now, guess the first boy's age. 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.