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 15
Recently Kevin had a party and because it was his birthday he wanted a mathematical cake!
He ordered a cake in the shape of a cube and had it completely iced (but of course they didn't ice the underneath because that just isn't very sensible).
He cut every side of the cake into three equal pieces, giving 27 slices of cake.
He ended up eating all of the pieces of cake that had exactly 2 sides with icing.
So, how many pieces did that leave for the guests?
Hint
How many pieces on the top layer had two sides with icing?
Answer
15 pieces.
Reasoning
On each layer there are 4 pieces with exactly two sides of icing.
Therefore Kevin ate 12 pieces, leaving 15 for the guests.
??
Puzzle 16
The BrainBashers Dictionary of Proverbs is running out of memory.
Below are four proverbs with their vowels missing and the remaining letters are grouped in fours.
dntb tthh ndth tfds y
trth wllt
bslw nchs ngbt slwr nchn gng
thnk frst ndth nspk
