### Brain Teasers

# One Eleventh

Arrange the digits 1, 1, 2, 3, 3, 4, 4, 5, and 7 to form a single fraction that equals 1/11

### Answer

One solutions is 4321/47531=1/11Hide Answer Show Answer

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## Comments

(1+1+2+3) x (3x4+4-5)÷7?

mayb i red it rong

mayb i red it rong

VERY clever!! another solution is 1234/13574

To kick this one off, it helps to realize that you have 9 digits to place, which can only mean a fraction of 4 digits over 5 because your multiplier is 11. In addition, 11 is a handy number because all multiples of 11 have similar digit sequences. To further narrow down the choices, you can eliminate any 11xx multiples because they will all lead to a 1 appearing in the denominator. Next step is to eliminate "attractive" answers (1234 is an allowable digit sequence that begs to be tried for the numerator, and that did it for me), but I'm sure you can continue to eliminate options if you don't intuitively look for attractive answers.

To kick this one off, it helps to realize that you have 9 digits to place, which can only mean a fraction of 4 digits over 5 because your multiplier is 11. In addition, 11 is a handy number because all multiples of 11 have similar digit sequences. To further narrow down the choices, you can eliminate any 11xx multiples because they will all lead to a 1 appearing in the denominator. Next step is to eliminate "attractive" answers (1234 is an allowable digit sequence that begs to be tried for the numerator, and that did it for me), but I'm sure you can continue to eliminate options if you don't intuitively look for attractive answers.

Perhaps the problem would be clearer if you expressed it as:

"Arrange the digits 1, 1, 2, 3, 3, 4, 4, 5, and 7 to form a single fraction of two integers (numerator and denominator) that equals 1/ 11"

I ruled out a fraction of decimal numbers because a decimal is another fraction (does not fit the constraints on the solution), but it could be more explicit.

"Arrange the digits 1, 1, 2, 3, 3, 4, 4, 5, and 7 to form a single fraction of two integers (numerator and denominator) that equals 1/ 11"

I ruled out a fraction of decimal numbers because a decimal is another fraction (does not fit the constraints on the solution), but it could be more explicit.

huh?

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