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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Puzzle 14
A woman had three old coins: a silver dollar, a quarter, and a dime. Each coin was a little battered and had a piece missing. She found that exactly the same fraction had broken away from each coin.
What fraction of each was missing if the value of the remaining bits of coins was now exactly one dollar in total?
For this puzzle it can be assumed that 1/2 a coin is worth 1/2 of its value.
Hint
A dollar is 100 cents, a quarter is 25 cents and a dime is 10 cents.
Answer 7/27 of each coin was missing.
Reasoning
The original value of the three coins was 100 + 25 + 10 = 135 cents, and the new value was 100 cents.
Therefore, 35/135 = 7/27 of the original value has been removed.
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Puzzle 15
My BrainBashers electronic world atlas has developed a fault, I did a listing of miles from England to particular countries and here is the result:
Austria 1,800 miles
New Zealand 2,400 miles
Japan 1,200 miles
Brazil 1,400 miles
Hint
Vowels (AEIOU) and consonants are each worth a different number of miles.
Answer
2,200 miles.
Vowels (AEIOU) are worth 300 miles and consonants are worth 200 miles.
Double-Checking
Argentina has 4 vowels (AEIA = 4 x 300), and 5 consonants (RGNTN = 5 x 200), for a total of 1,200 + 1,000 = 1,200 miles.
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Puzzle 16
Three teachers were discussing how long they had been teaching.
Alex and Billie had been teaching for a total of 36 years. Charlie and Billie had been teaching for a total of 22 years. Charlie and Alex had been teaching for a total of 28 years.
How long had each been teaching?
