Goi's Fitness Forum

h wrote:

manyu882 wrote:the smallest amount is ((((((5+1)5+1)5+1)5+1)5+1)5+1= 19531

unfortunately, incorrect...
a bit smaller

h wrote:...care for another one?

common sense, but can you prove these?

a) prove that, of all rectangles having the same given perimeter P, the square encloses the biggest area.

b) prove that, of all rectangles having the same given area S, that of smallest perimeter is the square.

h wrote:...how about this:

In chess, is it possible for the knight to go (by allowable moves) from the lower left-hand corner of the board to the upper right-hand corner and in the process to light exactly once on each square?

note: look at a chessboard, then it's easy.

Canuck eh wrote:k, I've had monkeys and coconuts on the brain all day long, starting to bug me

Got as far as x=(4/5)^5*(1/5y+1)
where y=starting number and x the number just prior to the division in the morning...

Missing the key/trick to eliminate one of the variables...

h wrote:i think some of you will love this one:

prove that 22225555 + 55552222 is divisible by 7

Weib wrote:There are so many strength coaches out there, and will be more coaches in future..so whats the deal?
Just have to make it simple for people to understand..

h wrote:

Canuck eh wrote:k, I've had monkeys and coconuts on the brain all day long, starting to bug me

Got as far as x=(4/5)^5*(1/5y+1)
where y=starting number and x the number just prior to the division in the morning...

Missing the key/trick to eliminate one of the variables...

well, there's 2 (common) ways of going about solving this.
I suppose the easiest is to simply work backwards.

i.e.
N = the initial number of coconuts (before robbery)
n = the number of coconuts each man has received.

the number of coconuts in the last pile (before distribution) is: 5n + 1
the amount stolen by the last man is: (5n+1)/4
the # of coconuts before the last robbery is: 5(5n+1)/4 + 1

...

not so elegant, but if you work your way backwards, you'll eventually find a function of N in terms of n
N = f(n),
and you can work on finding n that satisfies the condition (N must be an integer, and as small as possible)

h wrote:i think this one is well-known:

an island is inhabited by five men and a pet monkey. One afternoon the men gathered a large pile of coconuts, which they proposed o divide equally among themselves the next morning.

during the night one of the men awoke and decided to help himself to his share of the nuts. in dividing them into five equal parts he found that there was one nut left over. This one he gave to the monkey. He then hid his one-fifth share, leaving the rest in a single pile. later during the night another man awoke with the same idea in mind. He went to the pile, divided it into five equal parts, and found that there was one coconut left over. This he gave to the monkey, and then he hid his one-fifth share, restoring the rest to one pile. during the same night each of the other three men arose, one at a time, and in ignorance of what had happened previously, went to the pile, and followed the same procedure. each time one coconut was left over, and it was given to the monkey.

The next morning, all five men went to the diminished nut pile and divided into five equal parts, finding that one nut remained over. what is the least number of coconuts the original pile could have contained?

h wrote:

h wrote:...how about this:

In chess, is it possible for the knight to go (by allowable moves) from the lower left-hand corner of the board to the upper right-hand corner and in the process to light exactly once on each square?

note: look at a chessboard, then it's easy.

i dunno if anyone's still working on this, or if anyone ever started...

but here's a hint: a1 and h8 are same color

Twxian wrote:chiu seem to be very free at work....

h wrote:no more monkeys... for now...


two brothers sold a herd of sheep which they owned. for each sheep they received as many $ as the number of sheep they sold (e.g. if they sold 4 sheep, they received $16, 9 sheep, then $91). the money was then divided in the following manner:

First, the older brother took $10, then the younger brother took $10, after which the older brother took another $10, and so on.

At the end of the division the younger brother, whose turn it was, found that there were fewer than $10 left, so he took what remained. To make the division just, the older brother gave the younger his penknife. How much was the penknife worth?