Bomb timer easy-med

For each 10 minutes , there are 10 instances in which the number of remaining minutes is equal to the number of remaining seconds in a minute. Here's an example of this for the first 10 minutes :

• $49:49$
• $48:48$
• $47:47$
• $46:46$
• $45:45$
• $44:44$
• $43:43$
• $42:42$
• $41:41$
• $40:40$

The rest of the instances occurs between 40-30 minutes , 30-20 minutes , 20-10 minutes , and 10-0 minutes .

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For each 10 minutes , there are also 5 instances in which the digits on the timer read the same when reversed. Here's an example of this for the first 10 minutes :

• $45:54$
• $43:34$
• $42:24$
• $41:14$
• $40:04$

Again, the rest of the instances occurs between 40-30 minutes , 30-20 minutes , 20-10 minutes , and 10-0 minutes .

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Here's what we know so far:

• There is 50 minutes remaining on the timer
• For each 10 minutes , there are 10 instances in which the number of minutes remaining is equal to the number of seconds remaining in a minute
• For each 10 minutes , there are 5 instances in which the digits on the timer read the same when reversed

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Now, let's do the calculations. Since there are 10 instances and an addition of 5 instances, we can add them up to get 15 instances. For each 10 minutes , 15 instances occur.

$10+5=15$

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Since there is 5 sets of 10 minutes in 50 minutes , we divide 50 by 10 and multiply the result by the number of instances in each 10 minutes , which is 15 . We also need to add 1 since time 00:00 is included.

$\frac{50}{10}$ $=5\cdot15=75+1=76$

There are 76 instances in total, with the adition of time 00:00

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Now that we know that there are 76 instances in total, we will be able to find out what the timer will display when the light blinks for the 70th time. Since it blinks only once for every instance, we need to find the 70th instance, in which the light will blink for the 70th time. Since the 70th instance happens between the 60th instance, which will happen at time 09:09 , and the 76th instance, which will happen at time 00:00 , We need to count from the time of the 60th instance until we get to the time of the 70th instance. Here's a list of instances in order from the 60th to the 76th :

• $09:09$

• $08:08$

• $07:07$

• $06:60$

• $06:06$

• $05:50$

• $05:05$

• $04:40$

• $04:04$

• $03:30$

• $03:03$

• $02:20$

• $02:02$

• $01:10$

• $01:01$

• $00:00$

If we start counting from the top to the bottom, we will eventually reach the 70th instance, which is time 03:03 .

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Now, the question specifically told us to add the digits in the 70th instance.

$0+3+0+3=6$

The answer to this question is 6