[BITList] THE DOOR

[HUGH]

Colin,

My answer is based on the assumption that there are n cells, each of which has a lock that is in the locked mode, and can be opened by a half turn of a (master) key, and the key is taken from lock to lock.

For all integers i = 1 to n, turn the key in lock ki, where k is an integer from 1 to n.

Locks numbered 1, 4, 9, 16 .... n squared are opened.

But there are only n locks.

So, for all integers i = 1 to n, turn the key in lock ki, where k is an integer from 1 to n, and ki is less than or equal to than n.

In a sense, the last step is a sort of sieve. The other problem uses a hidden sieve, all of these problems do, and it is disguised by the use of multiple steps and patter. 

Step 1: Think on a number.  I pick 11, and it's black.
Step 2: Click on the black button below the 5x5 grid.
Step 3. Click on one of the 9 coloured squares.
Step 4. Click on the house that contains your number.
Your number is 11 !!!!!!

In step 3, pick any square, the outcome will be the same. This step is a dummy.  Step 2 sieves out all the non-black numbers, so 7, 8, 11, 19 and 24 are carried through. These sets of 5 numbers are each placed in a set that will appear in a house at step 4.  Each set contains ONE number of each colour, so the house with 11 in it also has
1, 4, 12, 13 and 30, each of these a different colour.  Not surprisingly, 11 is the only black number in that house.

Hugh.



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