Detect the Nearly Perfect Licence Plates

Question

Note: This is inspired by this question by @Willbeing where task was to count the number of perfect plates of a certain length, but it's slightly different.

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We call a perfect licence plate that plate whose text satisfies the following conditions:

• It consists of characters, which can either be uppercase letters([A-Z]) or digits([0-9])
• Summing the positions of its letters in the English alphabet, 1-indexed (i.e: A=1,B=2,...,Z=26) gives an integer n
• Getting each chunk of digits, summing them and then multiplying all the results gives the same result, n
• n is a perfect square (e.g: 49 (7²), 16 (4²))

A nearly perfect licence plate meets the conditions for a perfect licence plate, except that n is not a perfect square.

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Input

A string representing the text of the licence plate, taken as input in any standard form, except for hardcoding.

Output

If the given string represents a nearly perfect licence plate, return a truthy value (e.g: True / 1), otherwise return a falsy value (e.g: False / 0). Any standard form of output is accepted while taking note that this loopholes are strictly forbidden.

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Examples

licence plate -> output


A1B2C3 -> 1

A + B + C = 1 + 2 + 3 = 6
1 * 2 * 3 = 6 
6 is not a perfect square, 6 = 6 => nearly perfect plate

01G61 -> 1

(0 + 1) * (6 + 1) = 7
G = 7
7 is not a perfect square, 7 = 7 => nearly perfect plate

11BB2 -> 0

(1 + 1) * 2 = 4
B + B = 2 + 2 = 4
4 = 4, but 4 is the square of 2 => perfect license plate (not what we want)

67FF1 -> 0

(6 + 7) * 1 = 13
F + F = 6 + 6 = 12
12 != 13 => not perfect at all!

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Scoring

This is code-golf, so the shortest answer in bytes wins!

Answer 1

Jelly, 29 28 30 bytes

+1 byte to fix a bug spotted by ChristianSievers (incorrectly dealing with substrings of only zeros) +1 byte to fix false positives for "0", "00", ... found during above fixing (0 is a perfect square).

i@€ØAS;Ʋ$
e€ØAœpV€€LÐfS€P;0⁼Ç

Try it online!, or run tests

How?

i@€ØAS;Ʋ$ - Link 1: [letter-sum, letter-sum is perfect square?]: plate
i@€        - index of €ach char in plate [reversed @rguments] (1-based, 0 otherwise) in:
   ØA      -     uppercase alphabet
     S     - sum
         $ - last two links as a monad:
      ;    -     concatenate with:
       Ʋ  -         is square?

e€ØAœpV€€LÐfS€P;0⁼Ç - Main link: plate                        e.g. "11BB2"
    œp              - partition plate at truthy values of:
e€                  -     is in? for €ach char in plate:
  ØA                -         uppercase alphabet                   [['1','1'],[''],['2']]
      V€€           - evaluate for €ach for €ach                   [[1,1],[],[2]]
          Ðf        - filter keep:
         L          -     length                                   [[1,1],[2]]
            S€      - sum each                                     [2,2]
              P     - product                                      4
               ;0   - concatenate a zero                           [4,0]
                  Ç - last link (1) as a monad (taking plate)      [4,1]
                 ⁼  - equal? (non-vectorising)                     0

Answer 2

MATL, 36 34 33 35 bytes

3Y432YXU"@V!Usvp]GlY2&msy=wtQ:qUm~v

Try it at MATL Online

Explanation

        % Implicitly grab input as a string
3Y4     % Push the predefined literal '[A-Za-z]+' to the stack
32      % Push the literal 32 to the stack (ASCII for ' ')
YX      % Replace the matched regex with spaces (puts a space in place of all letters)
U       % Convert the string to a number. The spaces make it such that each group of
        % of consecutive digits is made into a number
"       % For each of these numbers
  @V!U  % Break it into digits
  s     % Sum the digits
  v     % Vertically concatenate the entire stack
  p     % Compute the product of this vector
]       % End of for loop
G       % Explicitly grab the input again
lY2     % Push the predefined literal 'ABCD....XYZ' to the stack
&m      % Check membership of each character in the input in this array and 
        % return an array that is 0 where it wasn't a letter and the index in 'ABC..XYZ'
        % when it was a letter
s       % Sum the resulting vector
y       % Duplicate the product of the sums of digits result
=       % Compare to the sum of letter indices result
w       % Flip the top two stack elements
Q       % Add one to this value (N)
t:      % Duplicate and compute the array [1...N]
q       % Subtract 1 from this array to yield [0...N-1]
U       % Square all elements to create all perfect squares between 1 and N^2
m~      % Check to ensure that N is not in the array of perfect squares
v       % Vertically concatenate the stack.
        % Implicitly display the truthy/falsey result

Answer 3

Python 2, 120 118 bytes

s=t=p=0;r=1
for n in input():
 h=int(n,36)
 if h>9:s+=h-9;r*=t**p
 p=h<10;t=(t+h)*p
print(s==r*t**p)&(int(s**.5)**2<s)

Try it online!

Interprets each character as a number in base-36 (h). Converts to decimal and adds to the sum if h>9 (meaning it's a letter), otherwise adds to a variable which gets multiplied to form the running product later.

Answer 4

Perl 5, 80 bytes

79 bytes of code + -p flag.

$.*=eval s/./+$&/gr for/\d+/g;$t-=64-ord for/\pl/g;$_=$.==$t&&($.**.5|0)**2!=$.

Try it online!

$.*=eval s/./+$&/gr for/\d+/g; multiplies the sums of consecutive digits. (I'm using $. because it's initial value is 1, which mean it's the neutral element for multiplication). More precisely, for each chunk of digits (for/\d+/g), s/./+$&/gr places a + before each digit, then the string is evaluated, and multiplied with the current product.
Secondly, $t-=64-ord for/\pl/g; sums in $t each letter (for/\pl/g). (ord return the ascii code for the letter, and 64-.. makes it be between 1 and 26.
Finally, $.==$t checks that both values are the same, and ($.**.5|0)**2!=$. that it's nor a perfect square.

Answer 5

Python 2, 267 207 bytes

^{Saved 60 bytes thanks to ovs}

import re
def g(l):a=reduce(lambda a,b:a*b,[sum(map(int,list(i)))for i in re.sub(r'\D',' ',l).split()],1);return a==sum(sum(k)for k in[[ord(i)-64for i in x]for x in re.sub(r'\d',' ',l).split()])and a**.5%1>0

Function with usage: print(g('A1B2C3'))

Try it online!

Answer 6

Python 3, 163 156 155 164 161 bytes

from math import*
m=1;s=t=p=0
for x in input():
 try:t+=int(x);p=1
 except:m*=[1,t][p];p=t=0;s+=ord(x.upper())-64
if p:m*=t
print(m==s and sqrt(m)!=int(sqrt(m)))

Try it online!

• saved 7 bytes thanks to Jonathan and Shooqie
• saved 1 byte: Also Fixed the false positive issue. Thanks to Jonathan for pointing it out!
• added 11 bytes: Previous edit was wrong(the multiplication of sum of digit was going on in an unwanted loop)

Answer 7

Retina, 143 bytes

Returns 1 for true, 0 for false

[1-9]
$*
10|01
1
S_`(\D)
O`
{`1(?=1*\n(1+))
$1
)2=`1+\n

[J-S]
1$+
[T-Z]
2$+
T`0L`ddd
1>`\d+\n?
$*
^((?(1)((?(2)\2(11)|111))|1))*\n

^(1*)\n\1$

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Explanation:

[1-9]
$*
10|01
1

First, we replace all non-zero digits with their unary representation. We remove any zeroes with an adjacent digit so that they don't affect our unary operations

S_`(\D)

Split the resulting string on letters, being careful to exclude empty lines (this is a problem when two letters are consecutive AA).

O`
{`1(?=1*\n(1+))
$1
)2=`1+\n

Sort the string lexicographically. Then repeatedly do the following:

1) Replace each 1 with the number of 1s on the following line (this mimics multiplication)

2) Remove the second line of 1s

[J-S]
1$+
[T-Z]
2$+
T`0L`ddd

Replace letters J-S with 1J, 1K, etc. and replace letters T-Z with 2T, 2U, etc. Then, replace each of the groups A-I, J-S, and T-Z with 1-9. We will be left with the numerical value of each letter (eg. 13 for M).

1>`\d+\n?
$*

Convert every line but the first into unary (the first line is already in unary). Concatenate these lines. We are now left with a string of the form <product of digits>\n<sum of letters>.

^((?(1)((?(2)\2(11)|111))|1))*\n

Replace a square number with the empty string. This uses the "difference tree" method.

^(1*)\n\1$

Return 1 if the two strings on either side of the \n match. Otherwise, return 0.