IBM Ponder This #239 · March 2018

Alice and Bob are given an interesting challenge. Alice will be given a random vowel (A, E, I, O, or U) in a room without Bob with six randomly set toggle (on/off) switches. She may change the state of at most one switch and then leave the room without talking to Bob. Bob must then enter the room and discover the secret vowel Alice was given.

Before Alice enters the room, she and Bob agree on a plan. Their strategy is to declare the unknown (as yet) vowel as a function of the new state of the switches.

What exactly is their suggestion?

Supply your answer as a 64-long string of vowels: the first representing when all six switches are off; the second representing when the first five are off and the last is on; ... until the last vowel representing when all six switches are on.

For example, a similar challenge with just three switches and three letters A, B, and C can be solved (why?) by AABCCBAC, which stands for:

A	A	B	C	C	B	A	C

0	0	0	0	1	1	1	1

0	0	1	1	0	0	1	1

0	1	0	1	0	1	0	1

Solution

Best opened after a real attempt

To be added.