From a basket of mangoes when counted in twos there was one extra, counted in threes there were two extra, counted in fours there were three extra, counted in fives there were four extra, counted in sixes there were five extra, but counted in sevens there were no extras.
At least how many mangoes were there in the basket?
119. The number has to be evenly divisible by seven for there to be no extras when counting in sevens, and it has to be odd in order for there to be one extra when counting by twos. It also can’t be evenly divisible by three through six. 119 is the first odd multiple of 7 that satisfies the requirements.
I’m a five letter word. Remove my last two letters and I’m a synonym of drag. My second and third letters form an exclamation and my first and second letters are a homophone with a number. What am I?
Towel. Tow is a synonym of drag, ow is an exclamation when you’re hurt (and far more appropriate in mixed company than the four-letter alternatives) and to is a homophone of two.
91. To get the number in the fourth column, you add the numbers in column 1 and 2, then multiply by the number in column 2. f(n,m) = (n + m) * m For example, f(2,3) = (2 + 3) * 3 = 15. Thus f(6,7) = (6 + 7) * 7 = 91
The next number in the series counts the previous numbers. Thus the first number is 1, which is one 1, or 11. To describe 11, you have two 1’s, or 21. Now you have one 2 and one 1, so the next number is 1211. The solution is to continue describing the previous number using only numbers.