## Problem of the Day #283: Bunny Tongues
*December 27, 2011*

*Posted by Seungln in : potd , trackback*

Saketh has three different bunnies, each with long tongues, just like this guy.

Saketh later discovers that these bunnies’ tongues grow or shrink every night with these following rules.

The length of Bunny 1′s tongue increases by 4 times the length of Bunny 2′s tongue, but decreases by 3 times the length of Bunny 3′s tongue.

The length of Bunny 2′s tongue increases by twice the length of Bunny 1′s tongue, but decreases by the length of Bunny 3′s tongue.

The length of Bunny 3′s tongue doubles, but decreases by twice the length of Bunny 1′s tongue.

However, Saketh notices that there seems to be no difference in the lengths of the tongues of each bunny between each day. What is the ratio of the lengths of the tongues of the bunnies? Express the ratio in the format (*length of the tongue of Bunny 1*):(*length of the tongue of Bunny 2*):(*length of the tongue of Bunny 3*).

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