Puzzle 165
Which are there more of …
… square feet in half a square mile or cubic yards in a cubic furlong?
Puzzle Copyright © Kevin Stone
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Hint
There are 3 feet in a yard, 1760 yards in a mile, and 8 furlongs in a mile.
Answer
Square feet in half a square mile.
Reasoning
There are 3 feet in a yard, 1760 yards in a mile, and 8 furlongs in a mile.
A mile is 1760 x 3 = 5280 feet in a mile.
A square mile is 5280 x 5280 = 27878400 square feet.
Therefore, half a square mile = 13,939,200 square feet.
A furlong is 1760 ÷ 8 = 220 yards.
Therefore, a cubic furlong is 220 x 220 x 220 = 10,648,000 cubic yards.
Puzzle 166
How many times can you take 7 away from 49?
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Hint
This is a trick question.
Answer
Once.
After which you will be taking 7 from 42!
Puzzle 167
A Proof That 2 = 1. Let A = B:
A = B
multiply by A on both sides:
A x A = A x B
subtract B x B from both sides:
A x A – B x B = A x B – B x B
factorise:
(A + B)(A – B) = B(A – B)
divide by (A – B) on both sides:
(A + B) = B
replace A with B:
B + B = B
factorise:
2B = B
divide by B on both sides:
2 = 1
Where lies the flaw in the logic?
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Answer
On line 4 we are dividing both sides by (A – B).
But we know that A = B, so A – B = 0.
Dividing by zero is undefined, so we are not allowed to do this.
Puzzle 168
What is the smallest positive integer which …
… when multiplied by 3 gives a number consisting of only 4's?
Puzzle Copyright © Kevin Stone
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Hint
Try working backwards.
Answer
148.
Reasoning
A number that is divisible by 3 has digits that add up to a number that is also divisible by 3 (for example, 123 is divisible by 3).
So we can look for the first number where 4 + 4 + 4 + 4 + 4 + … is divisible by 3, which is 4 + 4 + 4, and 444 ÷ 3 = 148.
Alternative Reasoning
Let's try the possible answers in order:
4 ÷ 3 = 1.3333
44 ÷ 3 = 14.6666
444 ÷ 3 = 148
Double-Checking
148 x 3 = 444.
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