Brain Teasers
Can You Guess the Number
Fred and Bob are sitting around, shooting the mathematical breeze, when they decide to play a game of "Guess the Number".
Fred tells Bob that he is thinking of a number between 13 and 1313.
Bob asks Fred if the number is below 500. Fred says, "Yes."
Bob asks Fred if the number is a perfect square. Fred says, "Yes."
Bob asks Fred if the number is a perfect cube. Fred says, "Yes."
Fred then tells Bob that one of his answers was incorrect and the number he is thinking of starts with an odd digit greater than 3.
What is the number that Fred is thinking of?
Fred tells Bob that he is thinking of a number between 13 and 1313.
Bob asks Fred if the number is below 500. Fred says, "Yes."
Bob asks Fred if the number is a perfect square. Fred says, "Yes."
Bob asks Fred if the number is a perfect cube. Fred says, "Yes."
Fred then tells Bob that one of his answers was incorrect and the number he is thinking of starts with an odd digit greater than 3.
What is the number that Fred is thinking of?
Answer
729To work it out, first separate the numbers at the 500 hundred point and find all of the perfect squares and perfect cubes.
13-499:
Perfect squares - 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484
Perfect cubes - 27, 64, 125, 216, 343
Both - 64
500-1313:
Perfect squares - 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296
Perfect cubes - 512, 729, 1000
Both - 729
In the lists of squares and cubes less than 500, there are no numbers that begin with an odd number greater than 3. Therefore, we can conclude that the first answer Fred gave was the incorrect one, and that 729 must be the answer.
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