# 28 Number Riddles

Numbers play a fascinating role in our lives, and they often hide intriguing patterns and mysteries.

If you enjoy solving puzzles and riddles, here are ten number riddles that will test your mathematical and logical skills.

Can you crack them all?

## Number Riddles

- What comes next in the sequence: 2, 3, 5, 7, 11, ?
- Half of 12 is 7. How?
- Three people check into a hotel room that costs $30. They each contribute $10. The hotel clerk realizes he overcharged them $5 and gives $5 to the bellboy to return. The bellboy, however, decides to keep $2 for himself and gives $1 back to each person. Now each person has paid $9, totaling $27. The bellboy has $2. Where is the missing dollar?
- If you multiply my age by 4 and then subtract 4, the result is the same as if you add 4 to my age and then multiply by 2. How old am I?
- I am a three-digit number. My tens digit is five more than my ones digit. My hundreds digit is eight less than my tens digit. What number am I?
- I am a number. When you multiply me by any other number, the result will always remain the same. What number am I?
- What is the smallest number that is evenly divisible by 12 that has the same sum of digits as 12?
- At what times between 3 and 4 o’clock are the hour and minute hands of a clock exactly overlapping?
- In a room of 23 people, what are the chances that two people have the same birthday?
- In a building, there are 100 floors. If 1/2 of 5 plus 1/4 of 4 equals the floor number, what is the floor?
- Ten years ago, I was twice as old as my son. In ten years, I will be 1.5 times his age. How old am I now?
- When the time is 3:15, what is the angle between the hour and minute hands of the clock?
- Three fishermen catch 3 fish in 3 minutes. At this rate, how many fishermen are needed to catch 60 fish in 60 minutes?
- I am thinking of two numbers. Their sum is 12, and their product is 35. What are the two numbers?
- What is the next time after 2:22 pm that the digits on a digital clock will form a palindrome (look the same forwards and backwards)?
- What is the only even prime number?
- If a book has 12345678910 pages, what is the total number of digits used to number the pages?
- A farmer has 17 sheep. All but 9 die. How many are left?
- I am a 3-digit number. My digits are all the same, and the sum of my digits is 27. What number am I?
- How many times in a day do the hour and minute hands of a clock overlap?
- You have some apples. If you divide them among 4 people, 3 apples remain. If you divide them among 3 people, 2 apples remain. What is the least number of apples you have?
- In the series 1, 4, 27, 16, ?, 36, what number should replace the question mark?
- Swap two digits of the number 1234 to make the highest possible number.
- Take half of 100, add 20, then divide by 2, and finally subtract 15. What number do you get?
- What is the next number in the series 1, 2, 4, 8, 16, ?
- What is the smallest number that becomes larger when you reverse its digits and then subtract the smaller number from the larger one?
- My age three years ago was three times what it was 15 years ago. How old am I?
- What is the largest 4-digit number in which all four digits are the same?

## Answers

- 13 (They are prime numbers).
- “Half of 12” is interpreted as “half of XII,” which is VII, the Roman numeral for 7.
- There is no missing dollar. The $27 total includes the $2 the bellboy kept. Breakdown: $25 for the room + $2 kept by the bellboy = $27.
- 4 years old. (4 * 4 – 4 = 4 + 4 * 2)
- 193. (3 + 5 = 8, 8 – 8 = 0, but the hundreds digit can’t be 0, so it’s 8 + 2 = 10, hence 193).
- Zero (0 * anything = 0).
- 48 (4 + 8 = 12, and 48 is divisible by 12).
- At approximately 3:16:21.82 (The minute hand is 360°/60 = 6° per minute, and the hour hand is 360°/12 = 0.5° per minute).
- About 50.7% (This is a well-known probability problem known as the “Birthday Paradox”).
- Floor 2.5 (1/2 of 5 is 2.5, and 1/4 of 4 is 1. Combined, they still make 2.5).
- I am 40 years old. (If my son is X years old, 10 years ago I was 2X and he was X-10. So now I am 2X+10 and he is X. In ten years, I will be 2X+20 and he will be X+10. 1.5 times X+10 equals 2X+20).
- 7.5 degrees (At 3:15, the hour hand is 7.5 degrees past the 3 o’clock mark).
- Still three fishermen. The rate of catching fish doesn’t change with the number of fishermen.
- The numbers are 5 and 7. (5 + 7 = 12, 5 * 7 = 35).
- 4:40 pm (The next palindromic time).
- 2 (It’s the only even number that is prime).
- 11 digits (1 for the first 9 pages, 2 each for the next 90, 3 each for the next 900, and so on).
- 9 sheep are left (All but 9 die, meaning 9 survive).
- 999 (Each digit is 9, and there are three of them).
- 22 times (They overlap approximately every 65 minutes, but not exactly every hour).
- 11 apples (11 % 4 = 3 and 11 % 3 = 2).
- 125 (The series alternates between squares and cubes: 13,22,33,42,53,6213,22,33,42,53,62).
- 4231 (Swapping the 1 and the 4).
- 40 ((100 / 2) + 20 = 70, then 70 / 2 = 35, and 35 – 15 = 20).
- 32 (Each number is double the previous one).
- 10 (When reversed to 01 and subtracted, 10 – 1 = 9).
- 24 years old (If x is my current age, then x – 3 = 3(x – 15)).
- 9999 (The largest 4-digit number with all digits the same).