So, my friend just said referring to an old calculator that it gives 14 * 2 as 92. It was meant to be just an example, but the equation raised a question in my mind whether in any number system will the equation hold good. So, I did some paper-work and found some interesting results while searching for the required number system.
The first point is to note that if the base is greater than 10, the number shall be less than 28 and if greater than 10, it shall greater than 10. While any system lower than 10 won’t allow for the digit 9. So the given equation can’t be correct anywhere.
LHS is 14 * 2, so the system has to be greater than the 4-base, for the digit 4 to occur. Let’s check out 5-base, here 14 * 2 is 33. Yes, now it becomes very clear that the equation is not valid in any system. You see that in the highest value among the possible number systems is 33. So, any possibility for numbers greater than 33 is not possible for 14*2.
Now,
- In 5-base system : 14*2=33
- In 6-base system : 14*2=32
- In 7-base system : 14*2=31
- In 8-base system : 14*2=30
- In 9-base system : 14*2=28
- In decimal system : 14*2=28
- In 11-base system : 14*2=28
- In 12-base system : 14*2=28
- In 13-base system : 14*2=28
- In 14-base system : 14*2=28
The most interesting fact is that for all systems greater than 8, the equation holds good. So, we have a new question, why only after 8?
Keep thinking!!
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