Numerical and logical headaches
The numerical Headaches and logics are Casse-tête S which consist in solving a diverting problem, where information seems to miss, and of which the resolution can be made thanks to calculation, the logic and/or the fine observation of the statement.
Numerical example of headache
By replacing each letter by a different figure, could you give a direction to the addition: SEND + MORE = MONEY?This type of numerical headache is called Cryptarithme.
Logical example of headache
On an isolated island 100 fishermen live. Some have the red eyes, others have the blue eyes, but this subject being taboo here, nobody knows his color of eyes. Moreover, they are seen only the day.January 1st, their chief their advertisement that as from this day, those which know that they have the red eyes will have to leave during the following night.
On which date, if it exists, all the fishermen with the red eyes will be parties, by supposing that they all are obeying and perfectly logics and that at the beginning, there is at least a fisherman who has the red eyes?
First day:
Assumption: only one red fisherman. He sees 99 blue: Certain its rougitude, the following day it leaves.
Assumption 2: two red fishermen. A R1 red sees 98 blue and 1 R2 red. If the R2 red does not leave the following day, it is that he did not see the day before 99 blue, and thus R1 acquires the certainty which he is red him too. As the reasoning applies to R1 as for R2, both leave the island the second jour.
Consequence: any fishermen seeing two red fishermen their bracket reasoning Ci above, and given with the third for him even according to their departure (it is thus blue) or of their parking: (it is thus him even red)
While generalizing, any conspicuous fisherman NR red fishermen will be able to be determined the Nth day according to the departure or not of the NR reds.
The fishermen with the red eyes will thus leave all units the night, being their number.
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