Sum of 10 numbers
Posted: Thu Jul 24, 2014 8:55 pm
Showed this maths trick to Rachel when I was in the Countdown audience recently :
RR to players:
Start with any two numbers, say 7 and 1, and write them in a column.
Add them to get 8, and put 8 in the third column.
Add 1 and 8 to get 9, put in 4th column.
8 + 9 = 17, so put 17 in the 5th column.
9 + 17 = 26, so put 26 into the 6th column.
Repeat this same process until you have 10 numbers in the column; 7, 1, 8, 9, 17, 26, 43, 69, 112, 181. (An example of a generalised "Fibonacci" sequence)
But .... before the 10th number has been entered, RR writes 473 on a card, lets the players sum the 10 numbers together, and
those selfsame 10 numbers add to 473 !
Start with any other two numbers, say 1 and 1 (THE Fibonacci sequence) :
1, 1, 2, 3, 5, 8, 13, 21 ..... - I can say the total of the first 10 numbers is 143 without writing the whole list.
To the mathematicians among you, how and why does this trick work ?
RR to players:
Start with any two numbers, say 7 and 1, and write them in a column.
Add them to get 8, and put 8 in the third column.
Add 1 and 8 to get 9, put in 4th column.
8 + 9 = 17, so put 17 in the 5th column.
9 + 17 = 26, so put 26 into the 6th column.
Repeat this same process until you have 10 numbers in the column; 7, 1, 8, 9, 17, 26, 43, 69, 112, 181. (An example of a generalised "Fibonacci" sequence)
But .... before the 10th number has been entered, RR writes 473 on a card, lets the players sum the 10 numbers together, and
those selfsame 10 numbers add to 473 !
Start with any other two numbers, say 1 and 1 (THE Fibonacci sequence) :
1, 1, 2, 3, 5, 8, 13, 21 ..... - I can say the total of the first 10 numbers is 143 without writing the whole list.
To the mathematicians among you, how and why does this trick work ?