A digital clock displays hours and minutes in 24-hour format (00:00 to 23:59). What is the only time of day where the sum of the digits representing the hours equals the sum of the digits representing the minutes, and the product of all four digits combined is 24?
03:83 is invalid, so let's analyze the digits: product is 24. Possible sets of 4 digits whose product is 24: e.g., 1, 3, 2, 4. Let's test hour 13 and minutes 24. Hour 1: 1+3=4. Minutes 24: 2+4=6 (Not equal). What about hour 23 and minutes 14? Product 2*3*1*4 = 24. Hour sum: 2+3=5. Minute sum: 1+4=5. Time is 23:14.
The digits are 2, 3, 1, and 4. Formed into a 24-hour time, it becomes 23:14. The hour digits are 2 and 3 (sum = 5). The minute digits are 1 and 4 (sum = 5). The product of all four digits is 2 x 3 x 1 x 4 = 24.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Medium. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
More logic riddles
A man is looking at a photograph of someone on the wall. His friend asks, 'Whose picture are you looking at?' The man replies: 'Brothers and sisters have I none, but that man's father is my father's son.' Who is in the photograph?
A wooden cube is painted completely red on all six of its faces. It is then sliced evenly into 27 smaller, identical cubes (3x3x3). How many of the smaller cubes have paint on exactly zero of their faces?
I am a two-digit whole number. My tens digit is twice as large as my units digit. When you add my two digits together, the sum is 9. What number am I?
A row goes: bunny, bunny, egg, bunny, bunny, egg, bunny, bunny. What comes next?
Four alchemists each bring a single potion to a council: two healing potions, one sleeping potion, and one poison. Alchemist A says, 'My potion is not poison.' Alchemist B says, 'Alchemist C brought a healing potion.' Alchemist C says, 'Alchemist D brought the poison.' Alchemist D says, 'Alchemist A is lying.' If exactly one alchemist is lying, who brought the poison?
A digital safe opens only when you enter a four-digit number where the first digit is half the second, the third digit is the sum of the first and second, and the fourth digit is twice the second. The digits are all unique and non-zero. What is the code?