Trapped in Ice Lake

Suppose that you are trapped on the surface of a frozen lake. The surface is so smooth and ideal that there is no friction at all. You cant make any grip on the ice and no wind is blowing to help you out. You have just a mobile phone with you which has got no reception disabling you to call for help.

How will you plan your escape before you freeze to death on the frozen lake?




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Peter was in the 2nd bedroom.
So was I.
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Peter was in the bathroom with Christopher.
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David was in the kitchen.
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PS: The corpse was found in the Living Room.

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There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.