A spider is chasing an ant.
The spider is crawling counterclockwise at a
speed of 701 cm/min on the circumference of a circle with a diameter of 100
cm. The ant is crawling at a speed of
700 cm/min, also counterclockwise, on
a semicircle consisting of the upper
half of the spider’s circle plus a horizontal diameter.
At the start of the chase, the ant is at the left end of the diameter
and about to crawl along it, and the
spider is at the other end of the diameter and ready to start crawling along the circumference of the circle (to
which it is restricted). They commence crawling
at the same instant.
How many complete circuits of the circle must the
spider make before it catches the ant?
Idealize the problem by treating the
spider and the ant as points.
A and B are playing the game of bulls and cows. The rules of the game are as follows.
A selects a word with distinct letters and B has to find it. B is allowed a maximum of ten guesses. After every guess A tells B the number of Bulls and Cows in the word.
Bulls are letters which appear in the correct location, and cows are letters which appear, but not in their correct location
For example, if A selects a word BOLD while B guesses LOUD. Then A's reply would be 2 Bulls and 1 Cow.(O and D are in the correct place while L is not). Note that A only tells the number of Bulls and Cows. He does not tells which ones are cows and bulls.
A selected a six letter word. The game proceeded as follows:
1. FRIEND - 0 Bulls, 2 Cows
2. SQUARE - 0 Bulls, 2 Cows
3. GROUND - 0 Bulls, 3 Cows
4. FORMAT - 1 Bull, 0 Cows
5. TRAVEL - 1 Bull, 1 Cow
6. FORMAL - 0 Bulls, 0 Cows
7. FLIGHT - 2 Bulls, 0 Cows
8. SYMBOL - 0 Bulls, 1 Cow
9. FIGURE - 0 Bulls, 3 Cows
What is A's word?
(Assume that A's word is a valid English word and has 6 distinct letters.)