Lost Boarding Pass

July 21, 2020

We have today a fun little problem from probability:

On a sold-out flight, 100 people line up to board the plane. The first passenger in the line has lost his boarding pass but was allowed in, regardless. He takes a random seat. Each subsequent passenger takes his or her assigned seat if available, or a random unoccupied seat, otherwise. What is the probability that the last passenger to board the plane finds his seat unoccupied?

Your task is to determine the requested probability, either by reasoning mathematically or by writing a program to demonstrate the probability. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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Binary Concatenation

July 14, 2020

We have an interview question today:

The concatenation of the first four integers, written in binary, is 11011100; that is, 1 followed by 10 followed by 11 followed by 100. That concatenated number resolves to 220. A similar process can convert the concatenation of the first n binary numbers to a normal decimal number.

Your task is to compute the nth binary concatenation in the manner described above; report the result modulo 109+7, because the result grows so quickly. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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Trailing Zero-Bits

July 7, 2020

Today’s exercise indulges in some bit-hackery:

Given a positive integer, count the number of trailing zero-bits in its binary representation. For instance, 1810 = 100102, so it has 1 trailing zero-bit, and 4810 = 1100002, so it has 4 trailing zero-bits.

Your task is to write a program that counts the number of trailing zero-bits in the binary representation of a positive integer. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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Spelling Numbers

July 3, 2020

Your task is to write a program that lists all of the numbers from zero to one hundred, inclusive, in alphabetical order. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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