In the sequence formed by concatenating the digits 1, 2, 3, ..., i, i+1, ..., n what is the first appearance of k repetitions of the same digit?
For example, when k=3 the answer is:
11, 12: 111 (3 1s in a row).
Show with the same format for k = 2, 4, 5.
How far can you go?
Is there a pattern?
Note: k means "exactly k", so for k=2, the answer is not 11 because the next digit is another 1.
Let’s suppose that potatoes (by weight) are 99% water and 1%, well,
potato!
If we take a 100 pound bag of potatoes out and put them in the hot June sun, the water will begin to evaporate. If we monitor the moisture content (which starts at 99%, of course) and we weigh the potatoes just when the moisture content gets to 98% (precisely), then
how much will the potatoes weigh at that moment?
How much will they weigh when the moisture content is 50%?
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