Sum x Product

Computer Science Level 2

There are a few special numbers that are equal to the product of the sum of the digits and the product of the digits. For example, 135 → ( 1 + 3 + 5 ) × ( 1 × 3 × 5 ) = 135 135 \rightarrow (1 + 3 + 5) \times (1 \times 3 \times 5) = 135 . 1 1 also has this property. What is the only other positive integer less than 1000 1000 that also has this property?


The answer is 144.

Joshua Lowrance by Joshua Lowrance , 18, USA

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3 solutions

Steven Chase
Dec 2, 2018 
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# https://brilliant.org/problems/sum-x-product/

for j in range(1,1000):

    hunds = j / 100
    tens = (j - 100*hunds) / 10
    ones = j - 100*hunds - 10*tens

    q = (hunds + tens + ones) * (hunds * tens * ones)

    if q == j:
        print j

# Results
#135
#144

2 Helpful 0 Interesting 0 Brilliant 0 Confused

You used which software?

Mr. India - 2 years, 3 months ago

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It is Python

Steven Chase - 2 years, 3 months ago

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Ok thank you.will try to learn it!

Mr. India - 2 years, 3 months ago
David Stiff
Jan 18, 2019 
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for i in range(1001):
    numbers = [num for num in str(i)]
    sum = 0
    product = 1
    for num in numbers:
        sum += int(num)
        product *= int(num)
    if sum*product == i:
        print(i) 

# This yielded a result of 0, 1, 135, and 144
# However, since we have already been told that 1 and 135 are candidates, and that we are looking for a positive integer,
# our final answer will be 144

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Joshua Lowrance
Nov 27, 2018

144 → ( 1 + 4 + 4 ) × ( 1 × 4 × 4 ) = 144 144 \rightarrow (1 + 4 + 4) \times (1 \times 4 \times 4) = 144 . Also view this OEIS page .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

What is this page?

Mr. India - 2 years, 3 months ago

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On the right hand side, it has the numbers 1 to 1000, and on the left it has the number you get when you multiply the sum of the digits to the product of the digits.

Joshua Lowrance - 2 years, 3 months ago

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Oh, i didn't see the right.

Mr. India - 2 years, 3 months ago

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