Riddles on traviscj/blog

snack buying

Mon, 13 Nov 2017 07:01:25 +0000

I got this text message from my father-in-law:

Ok. Soda 1.50 Chocolate bar 1.00 Gum 0.10 Jelly Bean .05

Have to buy exactly 14 items and spend $10

At least one of each.

There are 4 diff combos. (Order: soda, chocolate, gum and jelly bean)

Got 5-2-3-4 3-5-4-2

Can’t get others. Any ideas? :)

I whipped up this solution to check in python:

#!/usr/bin/python3
# created_at: 2017-11-13 13:53:19 -0800

def main():
    solutions = 0
    for si in range(1,7):
        for ci in range(1,11):
            for gi in range(1,101):
                for ji in range(1,201):
                    total = si*150 + ci*100 + gi*10 + ji*5
                    items = si + ci + gi + ji
                    if total == 1000 and items == 14:
                        print(si,ci,gi,ji, total, items)
                        solutions += 1
    print(solutions)

if __name__ == "__main__":
    main()

The core of this solution is the check

some tips for project euler problems

Sat, 26 Jan 2013 00:00:00 +0000

I wanted to make a list of a few tips on solving Project Euler problems that have been helpful for me while I solve them. These are general principles, even though I do most of my Project Euler coding in Python.

Without further ado:

If the problem is asking for something concerning the number of digits, typically this indicates that the use of the $\log n$ function is warranted.
If the problem is asking for the last few digits, modulo arithmetic might speed it up considerably.
Some might consider this cheating, but looking up some small numbers in the Online Encyclopedia of Integer Sequences is occasionally pretty helpful.
Many problems boil down to: Find numbers with property $X$ and property $Y$. Two solutions are:
- Brute force: Try all numbers with tests of property $X$ and $Y$.
- Find numbers with property $X$ and filter by a test of property $Y$.
- Find numbers with property $Y$ and filter by a test of property $X$.
- Find the set of numbers with property $X$ and the set of numbers with property $Y$. Compute their intersection.

I’ve found that it’s sometimes hard to predict which one will end up being the fastest. It depends on the relative speed of the tests and the generators, and the frequency of finding numbers which have that property.

a trig problem solved in MATLAB

Wed, 01 Feb 2012 00:00:00 +0000

I came across this post. The basic idea is the guy wants to maximize $L_1+L_2$ constrained to this box, where $L_i$ is the length of beam $i$. It’s constrained to be a 61 cmx61 cm box, but one beam must start from 10cm up from the bottom right corner and the beams must meet at a point along the top of the box. I added the further assumption that the other beam must end in the bottom left corner.