A friend of mine drove from Aardvark to Beeville.
On the first day they travelled 1/3 of the distance.
On day two they travelled 1/2 of the remaining distance.
On day three they travelled 2/3 of the remaining distance.
On day four, after covering 3/4 of the remaining distance, they were still 5 miles away from Beeville.
How many miles had they covered so far?
[Ref: ZNKP] Copyright © Kevin Stone
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Hint: Try working backwards.
The total trip was 180 miles. Working backwards:
Day 4: travelled 3/4 leaving 5 miles, which means that 5 miles is 1/4, so 20 miles were left at the start of Day 4.
Day 3: travelled 2/3 leaving 20 miles, which means that 20 miles is 1/3, so 60 miles were left at the start of Day 3.
Day 2: travelled 1/2 leaving 60 miles, which means that 60 miles is 1/2, so 120 miles were left at the start of Day 2.
Day 1: travelled 1/3 leaving 120 miles, which means that 120 miles is 2/3, so 180 miles were left at the start of Day 1.
Of the 180 miles overall, 175 were covered in the 4 days.
Imagine a grid comprising 20 X 20 squares.
How many squares, of any size, in total?
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Hint: How many 1x1 squares are there, how many 2x2?
There is one 20x20, four 19x19, nine 18x18, sixteen 17x17, etc. The sum of the counts is 1 + 4 + 9 + 16 + 25 + 36 + ... + 400 = 2870.
My local library decided to hand out some of its old books to the 1,400 people who lived in the town.
To each library member they offered 6 books, and to each non-member they offered 4 books.
If only half of the members, and three quarters of the non-members, accepted the books, how many books were given away?
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Hint: It didn't matter how many library members or non-members there were.
Answer: 4,200 books.
It doesn't matter how many library members there were as 1/2 of them accepted the books, and each accepted 6 books, which is 3 books per member on average.
Similarly it doesn't matter how many non-members there were as 3/4 of them accepted the books, and each accepted 4 books, which is again 3 books per non-member on average.
So both the members and non-members accepted, on average, 3 books each. And 1400 * 3 = 4200.
Here is a curious grid, the sums of the shapes are shown at the end the row and at the base of each column.
What is the missing sum? What are the different shapes worth?
[Ref: ZJFC] Copyright © Kevin Stone
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Hint: The square is worth 7.
Square = 7
Triangle = 9
Circle = 12
Arrow = 3