Ready for a new challenge? These number riddles mix clever math twists with logical reasoning to keep you thinking. Take your time, look for patterns, and enjoy the puzzle hunt!
Number riddles
#Riddle 1:
I’m a two-digit number that equals 3 × (sum of my digits). What number am I?
Answer:
27. Let the digits be 2 and 7: sum = 2+7 = 9; 3×9 = 27.
#Riddle 2:
A number multiplied by 3 equals that number plus 24. What is the number?
Answer:
12. Let the number be x: 3x = x + 24 → 2x = 24 → x = 12.
#Riddle 3:
Find the smallest positive integer that leaves remainders 1, 2, 3 when divided by 2, 3, 4 respectively.
Answer:
11. We need x ≡ 1 (mod 2), x ≡ 2 (mod 3), x ≡ 3 (mod 4). That means x+1 is divisible by lcm(2,3,4)=12, so smallest is 11.
#Riddle 4:
I’m a two-digit number. My tens digit is one more than my ones digit, and the whole number equals 6 × (sum of my digits). What am I?
Answer:
54. Let ones = o, tens = o+1. Number = 10(o+1)+o = 11o+10. Sum digits = 2o+1. Equation: 11o+10 = 6(2o+1) = 12o+6 → o = 4 → number = 54.
#Riddle 5:
Three consecutive positive integers multiply to 120. Which integers are they?
Answer:
4, 5, 6. 4×5×6 = 120.
#Riddle 6:
A number plus half of itself equals 150. What is the number?
Answer:
100. Let x be the number: x + x/2 = 150 → (3/2)x = 150 → x = 150 × (2/3) = 100.
#Riddle 7:
I’m a cube less than 1000 whose digits add to 9. What am I?
Answer:
216. 6³ = 216 and 2+1+6 = 9.
#Riddle 8:
Move my first digit to the end and you get 3 × me. I’m a six-digit cyclic number. What am I?
Answer:
142857. 142857 × 3 = 428571, which is the original number with the first digit moved to the end. (Classic cyclic number from 1/7.)
#Riddle 9:
What is the smallest positive integer divisible by every integer from 1 to 10?
Answer:
2520. lcm(1..10) = 2520.
#Riddle 10:
I’m a two-digit number equal to the square of the sum of my digits. What number am I?
Answer:
81. Sum of digits of 81 is 8+1 = 9; 9² = 81.
#Riddle 11:
What is the smallest integer > 1 that is both a perfect square and a perfect cube?
Answer:
64. Numbers that are both square and cube are sixth powers. Smallest >1 is 2⁶ = 64.
#Riddle 12:
What is the smallest even perfect number?
Answer:
6. The smallest even perfect number is 6 (1 + 2 + 3 = 6).
#Riddle 13:
I’m a three-digit number. My digits add to 9, and if you add 198 to me you get my digits reversed. What number am I?
Answer:
153. Let number be 100a+10b+c. Adding 198 gives reversed digits, so 100a+10b+c +198 = 100c+10b+a → 99(c−a) = 198 → c−a = 2. Also a+b+c = 9 → 2a + b = 7. One solution: a=1, b=5, c=3 → 153. Check: 153 + 198 = 351.
#Riddle 14:
Find the (nontrivial) positive integer that equals the sum of the factorials of its digits.
Answer:
145. 1! + 4! + 5! = 1 + 24 + 120 = 145. (Nontrivial example; 1 and 2 are trivial cases since 1! =1, 2! =2.)
#Riddle 15:
The sum of the first n positive integers is 5050. What is n?
Answer:
100. Sum 1..n = n(n+1)/2 = 5050 → n(n+1) = 10,100. Recognize n=100 since 100×101/2 = 5050.
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