Today Puzzle #714
Puzzle No. 714鈥� Thursday 9 April 2020
Lockdown is getting a bit tiresome so my partner and I are finding ever more adventurous ways to pass the time. For instance, in the mornings I now ask my partner for help buttoning up my shirt. The shirt has 7 buttons and we do the buttons up from top to bottom, taking it in turns. The rule for a turn is that we can either fasten one single button or we can fasten two adjacent buttons. So far we have managed a different sequence of buttoning every morning. How many days will it take to go through every possible buttoning sequence?
Today’s #PuzzleForToday has been set by Hugh Hunt, Reader in Engineering Dynamics and Vibration at Trinity College, Cambridge
Click here for the answer
21
Look for a pattern for increasing number of buttons:
1 button has 1 pattern.
2 buttons has 2 patterns being 11,2
3 buttons has 3 patterns being 111,12,21
4 buttons has 5 patterns being 1111,112,121,211,22
5 buttons has 8 patterns being 11111,1112,1121,1211,2111,122,212,221
6 buttons has 13 patterns being
111111,11112,11121,11211,12111,21111,1122,1212,1221,2112,2121,2211,222
7 buttons has 21 patterns being
1111111,111112,111121,111211,112111,121111,211111,11122,11212,11221,12112,12121,12211,21112,21121,21211,22111,1222,2122,2212,2221
Note that this is the Fibonacci sequence – which is neat to prove!
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