Puzzle 109
Can you find every occurrence of the word JUNE that appears in this grid (horizontally, vertically, or diagonally)?
The hint will reveal the number of times it occurs, but where are they?
Note: this puzzle is not interactive, and the letters cannot be selected.
Puzzle Copyright © Kevin Stone
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Hint
The word JUNE appears 62 times.
Answer
The word JUNE appears 62 times.
Puzzle 111
Last week I spent half of my money on a new jacket, and then I spent half of that amount on some new trousers.
I was left with £32.94. How much did I spend?
Puzzle Copyright © Kevin Stone
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Hint
Try working backwards.
Answer
£98.82.
Reasoning
At the end I was left with £32.94, which was half of my remaining money, so before buying the trousers I must have had £65.88.
Again, this was half of my money, so before buying the jacket I must have had £131.76 at the start.
As I now had £32.94 remaining, I must have spent £98.82.
Double-Checking
I started with £131.76, and I spent £65.88 on a new jacket, and then £32.94 on the trousers, a total spend of £98.82.
Puzzle 112
Can you find three consecutive odd numbers that …
… total 7,644,585 when multiplied together?
Puzzle Copyright © Kevin Stone
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Hint
Try starting with the cube root of the number.
Answer
195 x 197 x 199.
Reasoning
Since we're after three numbers that multiply together, a good place to start is the cube root of 7,644,585, which is roughly 196.99.
Let's try dividing by the closest odd number to 196.99:
7644585 ÷ 197 = 38805
We're now after whole divisors of 38,805, so trying either odd number either side of 197 might work.
Trying either 195 or 199 gives the answer.
Double-Checking
195 x 197 x 199 = 7,644,585
Note
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.
