# A certain number has three digits. The sum of the three digits equals 36 times this number. Seven times the left digit plus 9 is equal to 5 times the sum of the two other digits. 8 times the second digit minus 9 is equal to the sum of the first and third. What is the number?

Discuss this Riddle in the comments below.

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I think what the author meant to say was “36 times the sum of the three digits equals this number” because as stated, this is impossible. The current statement means:

[x=digit 1, y=digit 2, z=digit 3]

The number –> #=100x+10y+z

The sum of the digits equals 36 times the number–> x+y+z=36#

Which would mean that 36(100x+10y+z)=x+y+z

The above equation is only true if x, y, and z are all equal to 0, making the “number” 000 which does not fulfill the rest of the riddle.

However the corrected statement, “36 times the sum of the three digits equals this number” would mean:

#=100x+10y+z=36(x+y+z)

Which can in fact be fulfilled by the digits 3, 2, and 4 and also agree with the rest of the riddle.

Thank you. Thank you very much.

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• Ron

Whoa.

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