Mathematical Puzzles 

Workings

Hint
It will take a while to check 1 x 7, 2 x 7, 3 x 7. What do we know about the answer?

Answer
63,492 x 7 = 444,444

Reasoning
We can work backwards, as we know that the number multiplied by 7 has only 4's. We can try the following:
      4 ÷ 7 ≈ 0.57     x
     44 ÷ 7 ≈ 6.29     x
    444 ÷ 7 ≈ 63.43    x
  4,444 ÷ 7 ≈ 634.86   x
 44,444 ÷ 7 ≈ 6,349.14 x
444,444 ÷ 7 = 63,492

Workings

Hint
The cube root of the given number is a good starting point.

Answer
71, 73, 79.

Reasoning
The cube root of 409,457 is around 74.

The closest consecutive prime numbers to 74 are: 61, 67, 71, 73, 79, 83, 89, 97.

Using a calculator, it is quickly seen that the answer can only be found using 71, 73 and 79.

Workings

Hint
There are 2.54cm in an inch.

Answer
250 centimetres.

Reasoning
One inch = 2.54cm.

And 1 foot = 12 inches = 30.48cm.

So, 8 feet = 243.84cm.

Workings

Hint
Work out how many each can eat in one minute.

Answer
53 minutes.

Reasoning
In one minute, Eddie eats 11 bananas (= 110 ÷ 10).

In one minute, Hugo eats 7 bananas (= 56 ÷ 8).

So in total, they eat 18 bananas every minute.

So it will take 954 ÷ 18 = 53 minutes.