Schools Mathematics Grand Challenge
First Week's Puzzles
The first problem was:
As I was going to St. Ives
I met a man with seven wives,
Each wife had seven sacks,
Each sack had seven cats,
Each cat had seven kits:
kits, cats, sacks and wives,
How many, in total, did I meet while going to St. Ives?
(You need to give the grand total (one number) of kits+cats+sacks+wives)
You were asked for the total number of kits, cats, sacks and wives.
Wives: Total number of wives = 7
Sacks: Each wife has 7 so total number of sacks = 7x7 = 7^2
Cats: Each sack has 7 cats so total number of cats = 7x7x7 = 7^3
Kits: Again, each cat has 7 kits so total number of kits = 7x7x7x7 = 7^4
Hence the grand total of kits+cats+sacks+wives is 7+7^2+7^3+7^4 = 2800.
The second problem was:
Fifteen years ago, my mother's age was three
times my age. She is now twice my age. What age
am I now?
Let X be my age and Y be my mother's age.
We have two pieces of information, both of which
we should use.
My mothers age is twice my age. This means that
Y = 2X
15 years ago my mother's age was three
times my age. This means that
Y - 15 = 3(X - 15)
But Y = 2X so
2X - 15 = 3X - 45
X = 30.
So, my age is thirty.