Question

A 24-hour alarm clock is set to beep once when the sum of the digits is 11 (for example 12:26), and twice if the sum of digits is 22 (for example 17:59). How many beeps can be heard in a 24-hour cycle (00:00 – 23:59)?

Answer 1

Given :  A 24-hour alarm clock is set to beep once when the sum of the digits is 11 (for example 12:26), and twice if the sum of digits is 22 (for example 17:59).

To Find :  How many beeps can be heard in a 24-hour cycle (00:00 – 23:59)?

Solution:

Sum of minutes can maximum be  5+ 9 = 14

Sum of Hrs  can be maximum 1+9 = 10

Hour 00    

Minutes 29 , 38 , 47  56  - 4 Beeps

Hour 01 , 10    

Minutes 28 , 37 , 46 ,   55  - 2 * 4 = 8 Beeps

Hour 02 , 11  , 20  

Minutes  09 , 18 ,27, 36 , 45 ,   54  - 3 * 6 = 18 Beeps

Hour 03  , 12 , 21

Minutes  08,  17 ,26, 35 , 44 ,   53  -  3 * 6 = 18 Beeps

Hour 04  , 13 , 22

Minutes  07,  16 ,25, 34 , 43 , 52    -  3* 6 = 18 Beeps

Hour 05 , 14  , 23

Minutes  06,  15 ,24, 33 , 42 , 51    -  3 * 6 = 18 Beeps

Hour 06  , 15

Minutes  05,  14 ,23, 32 , 41 , 50    -  2 * 6 = 12 Beeps

Hour 07  , 16  

Minutes  04,  13 ,22, 31 , 40      -  2 * 5 = 10 Beeps

Hour 08 , 17

Minutes  03,  12 ,21, 30     - 2 *4 = 8  Beeps

Minutes  59     -  2 * 1 = 2  Beeps

Hour 09 , 18

Minutes  02,  11 , 20      -  2 *3 = 6  Beeps  

Minutes  49 , 58     -  2 *2* 2  = 8  Beeps  

Hour 19

Minutes  01,  10      -    2 Beeps  

Minutes  39 , 48 , 57     -  1 *2* 3  =6  Beeps  

Total Beeps  = 138 beeps

Learn More:

on a regular 12-hour digital clock how many times would be the ...

https://brainly.in/question/11722132