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Workings

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!

Workings

Hint
The answer is not 31.

Answer
The largest sum that can be made is 34.

Workings

Answer
There is no fool like an old fool.

Workings

Hint
The missing word is in these locations: lo---e, ---ch, s---he, ---er, va---e.

Answer
Cat.
loe  = locate ch   = catch she  = scathe er   = cater vae  = vacate