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There are two without three

There are two without three

In a distant kingdom, they don't know the number three. There it is counted like this: 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15…

What number will they use to indicate a quantity of things that we would count as 100?

Solution

When they are missing a figure, when they reach 4 they actually have 3 of ours, so their 10 is actually ours 9. Similarly, they skip a number between 12 and 14, so their 14 is our 12. Thus, they reach 29 when they actually have 26 objects (they jump 1 out of 10). However, they cannot use 30 or any of the numbers of this ten, because they do not know the 3, so the number that will follow 29 will be 40, equivalent to our 27 (suddenly we will "delay" 10 numbers).

In this way, when they reach 99, they will drag a difference of 10 for the decade from 29 to 40 and another 9 for the jumps they will have made in each ten (one for each figure of the tens, and another for the first ten of the numbers with a figure). His 99 will be equivalent to our 80. Another way of thinking would be that they have used all the pairs of figures between 0 and 9, not counting 3, which are 9 (with the 0 in front form those of a single figure ). That would make a total of numbers of 9 * 9 = 81, but as I have also counted 00, I am going for the number 80.

The case is that its 100 is ours 81. We only have to count 19 to reach 100. But if we add 19 numbers of yours, we must take into account that they do not count 103, nor 113, that is, in reality It is his 121 that is worth the same as for us 100.