A Weird Microwave
*A microwave interprets every unit as a seconds.
Pretend you have a microwave that every group of 100 you input in a number is one minute (130 would be 1 minutes 30 seconds and 90 would be 1 minute 30 seconds). The maximum number you can input in this microwave is 999. On an instruction manual on something you want to eat it says to microwave something for 12 minutes. You know that it will take more than one round of microwaving to get 12 minutes.
Assumptions: Repeats will count, 999, 421 and 421, 999 is two ways. But they are not answers to the problem.
Question: How many ways can you input times so that it will only take two rounds of microwaving?
Hint: The answer is a palindrome.
The answer is 898.
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1 solution
The maximum time you may insert is 999, which on this weird microwave is 10 minutes and 39 seconds. To microwave a 12 minute object you need 1 minute and 21 seconds more which is 121. Since repeats count you subtract ((999-120, 120 is the numbers that don't work below 999)/2, divided by two because a pair is 2 numbers)x2, times two is repeats), the number right below the minimum, to see how many solutions there are. you get 879, Now you can see 81=121 and that goes up to 99=139, which happens to be 19 times. 19x279 is 898 which is the answer.