1
vote
1answer
51 views

How Many of a Given Weekday Fall in a Month

A month can have either $31, 30$, or $28$ days excluding leap years. Suppose we want to know "how many Fridays are in a given month". By considering the maximal case where the first Friday falls on ...
3
votes
2answers
345 views

Frog Jump Problem

Lotus leaves are arranged around a circle. A Frog starts jumping from one leaf in the manner described below. In the first jump it skips one leaf,next jump it skips two,three the next jump ...
5
votes
3answers
949 views

Chameleons Riddle

There are 10 red, 11 blue, 12 green chameleons. Sometimes, two chameleons meet. If they are the same color, nothing happens. If they are different colors, they will both change to the third ...
2
votes
0answers
83 views

When does $n^2$ divide $2^n+1$? [duplicate]

Possible Duplicate: How many rationals of the form $\large \frac{2^n+1}{n^2}$ are integers? A friend of mine asked me this question over lunch, and it's been a week that I can't do ...
1
vote
1answer
156 views

A rule to determine the crossed out digit

Lets take any integer, $z=abc\cdots$, form the sum of its digits, $a+b+c+\cdots$, subtract this from $z$, cross out any one digit from the result, and denote the sum of the remaining digits by $w$. ...