Merica!

Computer Science Level 5

$\begin{array} { l l l l l l } & H & A & W & A & I & I \\ & & I & D & A & H & O \\ & & & I & O & W & A \\ + & & & O & H & I & O \\ \hline & S & T & A & T & E & S \\ \end{array}$

In the above expression, each letter stands for a single unique digit. Calculate $\overline{AEIOHWDST}$ .

Details and Assumptions

None of the word starts with $0$ .

Image Credit: Wikimedia Frydolin

Here are My CS Problems

The answer is 149350862.

3 solutions

Pranjal Jain
Mar 30, 2015

import re
import itertools

def solve(puzzle):
    words = re.findall('[A-Z]+', puzzle.upper())
    unique_characters = set(''.join(words))
    assert len(unique_characters) <= 10, 'Too many letters'
    first_letters = {word[0] for word in words}
    n = len(first_letters)
    sorted_characters = ''.join(first_letters) + \
        ''.join(unique_characters - first_letters)
    characters = tuple(ord(c) for c in sorted_characters)
    digits = tuple(ord(c) for c in '0123456789')
    zero = digits[0]
    for guess in itertools.permutations(digits, len(characters)):
        if zero not in guess[:n]:
            equation = puzzle.translate(dict(zip(characters, guess)))
            if eval(equation):
                return equation

if __name__ == '__main__':
    import sys
    for puzzle in sys.argv[1:]:
        print(puzzle)
        solution = solve(puzzle)
        if solution:
            print(solution)

This is a general solution for which I posted this problem. For more details, see this

from itertools import permutations
for i in permutations('0123456789'):
    x=''.join(i)
    H=x[0]
    A=x[1]
    W=x[2]
    I=x[3]
    D=x[4]
    O=x[5]
    W=x[6]
    S=x[7]
    T=x[8]
    E=x[9]
    if int(H+A+W+A+I+I)+int(I+D+A+H+O)+int(I+O+W+A)+int(O+H+I+O)==int(S+T+A+T+E+S):
        print(int(A+E+I+O+H+W+D+S+T))

Raghav for the win.

Raghav Vaidyanathan - 6 years, 2 months ago

I knew this one. This problem was just for introducing some Python 3.x

Pranjal Jain - 6 years, 2 months ago

Actually I don't know it.. I have just been copy pasting it from @Aditya Raut 's solution to solve everything.

Raghav Vaidyanathan - 6 years, 2 months ago

@Raghav Vaidyanathan – It just uses the different permutations of a string '0123456789'. Then join method is used to convert the permutation object to string. Now, randomly, all the letters are given a position. At the end, the condition is checked by converting string to int. Its easier to concatenate strings, thus conversion is followed by concatenation.

Pranjal Jain - 6 years, 2 months ago

A far more easier solution will be this .

Don't get angry at me Pranjal , it's just that I have bookmarked a lot of sites and now they are coming in handy !

A Former Brilliant Member - 6 years, 2 months ago

Deep Shah
Apr 1, 2015

Here is my C code.

#include<stdio.h>

void main()
{

    int sum,sum1;
    int a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z;

    for(a=1;a<10;a++)
    for(d=0;d<10;d++)
    for(e=0;e<10;e++)
    for(h=1;h<10;h++)
    for(i=1;i<10;i++)
    for(o=1;o<10;o++)
    for(s=1;s<10;s++)
    for(t=0;t<10;t++)
    for(w=0;w<10;w++)
    {
        sum = (h*100000+a*10000+w*1000+a*100+i*11);
        sum += (i*10000+d*1000+a*100+h*10+o);
        sum += (i*1000+o*100+w*10+a);
        sum += (o*1000+h*100+i*10+o);
        sum1 = (s*100000+t*10000+a*1000+t*100+e*10+s);
        if(a==d || a==e || a==h || a==i || a==o || a==s || a==t || a==w)
            continue;
        if(d==e || d==h || d==i || d==o || d==s || d==t || d==w)
            continue;
        if(e==h || e==i || e==o || e==s || e==t || e==w)
            continue;
        if(h==i || h==o || h==s || h==t || h==w)
            continue;
        if(i==o || i==s || i==t || i==w)
            continue;
        if(o==s || o==t || o==w)
            continue;
        if(s==t || s==w)
            continue;
        if(t==w)
            continue;
        if(sum==sum1)
        {
            printf("%d\n",a*100000000+e*10000000+i*1000000+o*100000+h*10000+w*1000+d*100+s*10+t);
        }
    }
    return;
}

Python is good but i like C.

Usually C/C++ are not of use while dealing with bigger numbers (due to lack of such data types). Thus, I have moved on to python recently.

Pranjal Jain - 6 years, 2 months ago

Brock Brown
Mar 30, 2015

Python 2.7:

from itertools import permutations as perms
problem = 'HAWAII+IDAHO+IOWA+OHIO==STATES'
chars = set(problem)
chars -= set(['+','='])
nonzero = 'HIOS'
decrypt = {'+':'+','=':'='}
def decode(guess):
    new = ''
    for c in problem:
        new = new + decrypt[c]
    return new
def goal(guess):
    index = 0
    for c in chars:
        decrypt[c] = str(guess[index])
        index += 1
        if index == 9:
            break
    for c in nonzero:
        if decrypt[c] == '0':
            return False
    new = decode(guess)
    return eval(new)
for guess in perms(xrange(10)):
    if goal(guess):
        answer = ''
        for c in 'AEIOHWDST':
            answer = answer + decrypt[c]
        print "Answer:", answer
        break

I'm pretty ashamed of needing to use 30 lines and 70 seconds of running time, but give me a break, I hit my head today on the road during a bicycle wreck and had a concussion. :P

Are you all right now ?

A Former Brilliant Member - 6 years, 2 months ago

Yeah, I feel a million times better. Thanks for asking.

Brock Brown - 6 years, 2 months ago

Merica!

Image Credit: Wikimedia Frydolin

Here are My CS Problems

The answer is 149350862.

3 solutions

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