Quiz Answer Key and Fun Facts
1. You are caught in a heavy thunderstorm downpour and you arrive at the infamous Haunted Mansion of Numbers. You open the rusty iron gate and are immediately confronted by this unfriendly square number. The reciprocal of this square number is the aesthetically elegant decimal number 0.01234567890123456789... Can you figure out this number? Algebraically, find the value of x if 1 / x = 0.01234567890123456789... [Hint: is this a 2-digit or a 3-digit number?]
2. The chilly wind makes you feel uncomfortable. It seems like a never-ending journey as you walk from the gate to the doorstep. Unsurprisingly, the entrance is guarded by a gigantic 10-digit number. This number contains all the digits from 0-9. Another amazing property of this number is that it is divisible by all positive integers from 1-16. Which of the following numbers best fits the description? [Hint: observe the last digits of the four numbers given]
3. As you walk down the dimly lit hallway, a putrid smell greets your nose. You sense that a number is hiding in the dark corner. This number only gives you one clue - he is the smallest square number that can be expressed as the sum of two consecutive prime numbers. Can you determine what is the value of this number? [Hint: consider the question: is 1 a prime number? ]
4. Upon entering the abandoned great hall, an unpleasant eerie sound echoes throughout the enormous room. You see this sinister number standing next to the fireplace decorated with pumpkins and skulls. This number can be expressed as the sum in three interesting expressions. In other words, find x if x = 1 + 2 + 3 + 4 + 567 + 89 = 123 + 456 + 78 + 9 = 9 + 87 + 6 + 543 + 21. [Hint: try to estimate the value of the number]
5. After descending the winding staircase, you arrive at the notorious dungeon. As your eyes adjust to the darkness, you notice that a number is standing between two stone gargoyles. This number is the product of three consecutive prime numbers; the first prime number being 11. Can you determine the number being described? [Hint: what are the second and third prime numbers?]
6. As you hurry down the seemingly endless passageway, your footsteps reverberating through the entire chamber. You stumble across this 5-digit number. This number is the sum of the following five numbers: the smallest 3-digit positive integer, the smallest 4-digit positive integer, the greatest 2-digit positive integer, the greatest 3-digit positive integer and the greatest 4-digit positive integer. Can you guess what is this number? [Hint: use approximation or clever algebraic manipulation to estimate the number, for example, 99 = 100 - 1]
7. You enter a high ceiling room full of dusty medieval paintings and antique furniture. The paranormal atmosphere sends shiver down your spine. The number that you meet is a two-digit number. If you divide it by 2, 3, 4 and 5, it gives you 1, 2, 3 and 4 as the remainders respectively. What is this number? [Hint: find the least common multiple for the numbers 2, 3, 4 and 5]
8. As you make you way to the next room, you hear a ghastly sound. You gaze out the window to examine the source. You observe that a number is wandering around the cemetery. This number is a 5-digit palindromic number and it is divisible by 3. Which of the following numbers has the described mathematical properties? [Hint: if the sum of the individual digits of a number is divisible by 3, then the number itself is divisible by 3]
9. Upon entering the mysterious octagonal room, the ominous silence of the room makes you uneasy so you decide to leave, but as you reach for the doorknob, you are stopped by this number. It is the smallest number that is divisible by all the integers from 1 - 10 except 7. Also, it is the sum of two consecutive prime numbers. What is this number? [Hint: this number is related to angular measurement in geometry]
10. After climbing up the spiral staircase, you arrive at the astronomical observatory. The thunderstorm has passed and you are greeted by this final number. This is the smallest 2-digit number, when its digits are reversed and the resulting number is either added to or subtracted from the original number, both operations will yield perfect squares. What is this special number? [Hint: determine the first few perfect squares]
Source: Author
Matthew_07
This quiz was reviewed by FunTrivia editor
crisw before going online.
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