471: Digits in Fibonacci

We all recognize the Fibonacci Sequence:  1, 1, 2, 3, 5, 8, 13, 21, ...
What is the units digit of the sixty-first Fibonacci number?

Is there a pattern?

1,1,2,3,5,8,13,21,... What is the final digit of the sixty-first Fibonacci number?

— James Tanton (@jamestanton) May 24, 2015

436: Whiteboards at NCTMBoston

Found this in the #NCTMBoston exhibit hall. What questions do you have? #mathchat
— David Wees (@davidwees) April 17, 2015

364: Yearly Numerology

Time and Chance

A deck contains 52 cards, 12 court cards, 4 suits, and 13 ranks.
A year contains 52 weeks, 12 months, and 4 seasons of 13 weeks.
If A=1, J=11, Q=12, and K=13, then the values in a deck of cards total 364.

What do you make of that?


The number of gifts given out in "The Twelve Days of Christmas"? 364
On what day of the song is the middle gift given?

359: Lines and Diagonals

There's sequences all over the place. What are they?

Does your sequence predict the 20th case?

And the 11th and 12th?

356: Partridge in a Number Tree

You know the song. "And a Partridge in a Pear tree." What patterns of numbers can we find here?

The first partridge.

If you look at the total gifts each day, what sequence of numbers is this?

Four Calling Birds, calling out numbers ...

How many different ways are there to find the total number of gifts given over the twelve days?

207: Sequence of a

Consider the sequence:   1, a , a², a³, ... , aⁿ

Is the median of that sequence more than, less than, or equal to a^n/2 ?

What values of a could make this a dodgy question?

69: Triangular Fibonacci Numbers

1, 3, 21, 55 only triangular Fibonacci numbers.

Any tetrahedral beyond 1?

1,144 only square Fib nmbrs. 1,3,21,55 only triangular Fib nmbrs. 2 only oblong Fib nmbr. 1,8 only cubes. (Weird!) Any tetrahedral beyond 1?
— James Tanton (@jamestanton) January 21, 2014

65: Square Fibonacci Numbers

What are the only square Fibonacci numbers?
How can we show that these are the only ones?

1,144 only square Fib nmbrs. 1,3,21,55 only triangular Fib nmbrs. 2 only oblong Fib nmbr. 1,8 only cubes. (Weird!) Any tetrahedral beyond 1?
— James Tanton (@jamestanton) January 21, 2014