Question 176031
First of all, Y cannot be {{{0}}} because it is
a leading digit, and U cannot be {{{0}}} because
That would make the sum {{{000}}}, which it can't be
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So, Y and U must be one of the digits 1-9
Also, UUU must be less than {{{999}}} since one
more would be 4 digits, not 3.
If UUU is less than {{{999}}}, that means
3 x YOU must be less than {{{333}}}. It can't be
{{{333}}}, because each digit must be different
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When I add up the units column which is U + U + U,
I still get U in the sum, UUU, but I must have a
carry which would be {{{10}}}, {{{20}}},{{{30}}},
{{{40}}} up to {{{90}}}.
First I'll say the carry is {{{10}}}
U + U + U = U + 10
3U = U + 10
2U = 10
U = 5 and
UUU = 555
Now I'll say the carry is {{{20}}}
U + U + U = U + 20
3U = U + 20
2U = 20
U = 10
This is 2 digits, and it needs to be 1
Also, any higher carrys, {{{30}}},{{{40}}}, etc
would also be 2 digits
So, U = 5 and the carry is {{{10}}}
I have 3 x YO5 = 555
I'll divide both sides by 3
YO5 = 555/3
YOU = 185
185 + 185 + 185 = 555 answer