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number puzzle
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i am thinking of a 3 figure number, if you add together its 3 digits and multiply by 12 you get 1 less than the number itself
what number am i thinking of
what number am i thinking of
Answers
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Morning bob and "well done" to Grace!
Solution: If the digits from left to right are X, Y and Z,
then 12(X + Y + Z) = 100X +10Y +Z -1
So 88X - 11Z = 2Y + 1
That is 11(8X - Z) = 2Y + 1
Hence 2Y + 1 has a factor of 11 (and must be odd), therefore Y = 5 and (8X - Z) = 1.
If then 8X = Z + 1 and these are single digits, we must have X = 1 and Z = 7.
The number XYZ is 157 (as Grace rightly says)
Solution: If the digits from left to right are X, Y and Z,
then 12(X + Y + Z) = 100X +10Y +Z -1
So 88X - 11Z = 2Y + 1
That is 11(8X - Z) = 2Y + 1
Hence 2Y + 1 has a factor of 11 (and must be odd), therefore Y = 5 and (8X - Z) = 1.
If then 8X = Z + 1 and these are single digits, we must have X = 1 and Z = 7.
The number XYZ is 157 (as Grace rightly says)
1 to 2 of 2
