A child attempts to open a five disc lock. He takes $5$ seconds to dial a particular number on the disc. if he does so for $5 $hours every day, Find Max number of days he would take to open the lock.

My Try: Since it is dial disc, total possible $5$ digit codes is $10^5$.

Since he takes $25$ seconds to dial a $5$ digit code, number of $5$ digit codes he tried in one day is $\frac{5 \times 60 \times 60}{25}=720$

Let $n$ be number of days, so

$$720n=10^5$$ $\implies$

$n=139$ days approx. But my book answer is $666$

Please tell where i went wrong?

  • $\begingroup$ Does he try a distinct combination every attempt? $\endgroup$ – Will Fisher Aug 29 '17 at 3:03
  • $\begingroup$ that is not specified in the question. I assumed it $\endgroup$ – Umesh shankar Aug 29 '17 at 3:04

You have two problems. The first is that the problem statement says it takes $5$ seconds to try a number, which I read as inputting all five characters. You have used $25$ thinking that it takes $5$ seconds to set each of $5$ characters. That is an English question, not a mathematical one, but it would reduce the time instead of increasing it. The second is there is nothing in the question as you have quoted it that tells us how many numbers are on the disc. As I read it he can try $3600$ codes per day. If I go backwards from the answer to ask the number of characters $k$ in the combination I am trying to solve $3600 \cdot 666=k^5$ then round up and I get $k=19$ which is a strange number of characters to use in the combination. In your reading I get $14$ characters to compensate for the fact that he doesn't try codes as fast. That is also a strange number to use in the combination. You are thinking correctly.

  • $\begingroup$ Also, any reasonable person would probably try 00000, 00001, 00002, etc. so you don't have to change all 5 discs every time ... but that would decrease the time even more ... $\endgroup$ – Bram28 Aug 29 '17 at 12:59

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