Can you fill in these boxes?

Within the 10 boxes above, each contains a distinct digit from 0 to 9 such that the product on the left equals to the sum on the right.

What is the maximum 3-digit value of this expression?


The answer is 972.

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2 solutions

The example solution for this would be: 1 8 × 5 4 = 7 0 9 + 2 6 3 = 972 \boxed{1}\boxed{8}\times \boxed{5}\boxed{4} = \boxed{7}\boxed{0}\boxed{9} + \boxed{2}\boxed{6}\boxed{3} = 972 .

You give the example but you don't explain how to arrive at it. Hence you do not show the reasoning and causes that determine it and hence , in order for the solution to be more complete and gain some insight in the approach and approximation of reasoning of like problems can you explain how to arrive at the answer , so to say anyway , even in a fast way , not being completely detailed , and just showing the general and also broad reasoning of it anyway ?

A A - 4 years, 11 months ago

25 x 70 = 914 + 836 = 1750 works as well, but is not accepted as correct answer...

Patrick Pfenning - 4 years, 11 months ago

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Thanks. Those who answered 972 have been marked correct.

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Calvin Lin Staff - 4 years, 11 months ago

Sorry, I forgot to say the Max. 3-digit value.

Worranat Pakornrat - 4 years, 11 months ago
Bryan Hung
Jul 29, 2016

I'm new to this part of the community so I'll just post my code here... Python of course...

import itertools
solList = []
for combo in itertools.permutations([0,1,2,3,4,5,6,7,8,9]): #Brute force basically.
    a = (combo[0]*10+combo[1])
    b = (combo[2]*10+combo[3])
    c = (combo[4]*100+combo[5]*10+combo[6])
    d = (combo[7]*100+combo[8]*10+combo[9])
    if a*b == c+d and len(str(c+d)) == 3: #Make sure both conditions hold
        solList.append(c+d) 

solList = sorted(solList) #Get largest value by sorting and reversing the list of solutions
solList.reverse()
print solList[0]

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