Math Riddles

Answer: For every pair of a truth and a lie his nose will shrink to 75 percent of its previous size prior to this truth and lie. So the correct answer is 0. As the number of times he tells a lie and the truth ((3/4)ⁿ) approaches infinity the length of his nose approaches 0.

Answer: The swan can travel 1/4 of the way to land then swim in a circular path around the center of the lake (the swan will be moving slightly faster around than the dog in their circles). Once the swan is as far as he can get away from the dog in his circle he can swim the remaining 3/4 of the way to shore. The dog must travel the radius of the lake time pi (radius * π) while the swan only has to travel 3/4 the radius four times slower (3/4 * radius * 4). So the swan will make it to the shore and fly before the dog reaches it.

Answer: Yes. Since the mountain climber would probably have an irregular rate it would be impossible to know when but he would be at the same spot at some point. If he could walk up and down the mountain at the same time he would have to cross himself at some point, and this would be the time at which he was in the same position.

Answer: The vine won't grow any vegetables, a tomato is a fruit! But the vine will grow 21 tomatoes.

Answer: The said number has all the numbers from 0-9 exactly once and what is special is they are in lexicographical order of their English words. Where 8,549,176,320 becomes eight-five-four-nine-one-seven-six-three-two-zero. ... The number contains all the digits from 0 to 9.