Puzzle 789
What are the next two letters in this sequence:
O · T · T · F · F · S · S · E · ? · ?
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Hint
This is a very common sequence.
Puzzle 790
How can you throw a ball such that it comes back?
No bounces are involved!
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Answer
Throw it up into the air!
Puzzle 791
In which sport do winners move backwards and losers move forwards?
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Puzzle 792
Can you find three consecutive odd numbers that …
… total 1,287 when multiplied together?
Puzzle Copyright © Kevin Stone
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Hint
There are two different methods, one involves a cube root, and the other doesn't require a calculator.
Answer
9 x 11 x 13.
Reasoning #1
We're after three numbers that multiply together, so a good place to start is the cube root of 1,287, which is roughly 10.88.
Let's try dividing by the closest odd number to 10.88:
1287 ÷ 11 = 117
We're now after whole divisors of 117. Trying the odd numbers either side of 11 might work.
Trying either 9 or 13 gives the answer:
9 x 11 x 13 = 1,287
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.
Reasoning #2
We after three numbers that multiply together, but none of these can end in 5 (otherwise our answer would end in 0 or 5).
So, they can only end in 7, 9, 1 (e.g. 87, 89, 91), or 9, 1, 3 (e.g. 89, 91, 93).
However, if they ended in 7, 9, 1, the answer would end in 3 (because 7 x 9 x 1 = 63).
Therefore, they end in 9, 1, and 3 (because 9 x 1 x 3 = 27).
The first numbers we can try are 9, 11, 13:
= 9 x 11 x 13
= 99 x 13
= 100 x 13 − 13
= 1300 − 13
= 1,287
A calculator is not required!
