Given that XY*8 = YYY ⇒⇒⇒ Where X and Y are digits So, X is equal to one of the digits from 1 to 9 and Y is one of the digits from 1 to 9 This can be solved as following YYY = 100Y + 10Y + Y = Y(100+10+1) = 111Y XY*8 = 8 (10X + Y) = 80X + 8Y ∴ 80X + 8Y = 111Y ∴ 80 X = 111Y - 8 Y ∴ 80 X = 103 Y
∴ Y = 80X/103 substitute with X = 1 to 9 X = 1 ⇒⇒⇒ Y = 0.77 ⇒⇒ unacceptable
X = 2 ⇒⇒⇒ Y = 1.55 ⇒⇒ unacceptable X = 3 ⇒⇒⇒ Y = 2.33 ⇒⇒ unacceptable X = 4 ⇒⇒⇒ Y = 3.11 ⇒⇒ unacceptable X = 5 ⇒⇒⇒ Y = 3.88 ⇒⇒ unacceptable X = 6 ⇒⇒⇒ Y = 4.66 ⇒⇒ unacceptable X = 7 ⇒⇒⇒ Y = 5.44 ⇒⇒ unacceptable X = 8 ⇒⇒⇒ Y = 6.21 ⇒⇒ unacceptable
X = 9 ⇒⇒⇒ Y = 6.99 ⇒⇒ unacceptable
So, The is no value of Y to achieve ⇒⇒ XY * 8 = YYY
================================================
I think the problem is as following:
Given that XY8 = YYY ⇒⇒⇒ Where X and Y are digits So, X is equal to one of the digits from 1 to 9 and Y is one of the digits from 1 to 9 This can be solved as following YYY = 100Y + 10Y + Y = Y(100+10+1) = 111Y XY8 = 100X + 10Y + 8 ∴ 100X + 10Y + 8 = 111Y ∴ 100x + 8 = 101Y ∴ Y = (100X + 8)/101 substitute with X = 1 to 9 X = 1 ⇒⇒⇒ Y = 1.07 ⇒⇒ unacceptable
X = 2 ⇒⇒⇒ Y = 2.06 ⇒⇒ unacceptable X = 3 ⇒⇒⇒ Y = 3.05 ⇒⇒ unacceptable X = 4 ⇒⇒⇒ Y = 4.04 ⇒⇒ unacceptable X = 5 ⇒⇒⇒ Y = 5.03 ⇒⇒ unacceptable X = 6 ⇒⇒⇒ Y = 6.02 ⇒⇒ unacceptable X = 7 ⇒⇒⇒ Y = 7.01 ⇒⇒ unacceptable X = 8 ⇒⇒⇒ Y = 8 ⇒⇒⇒ integer ⇒⇒ the correct answer
