Here are the solutions to Sunday’s puzzles. 

1) 24 sweets altogether

2) 5 and each brought 5 pumpkins.

3) Mrs Black gave apples, Ms White gave sweets, Mr Brown gave oranges and Ms Gray
gave monkey nuts.

4) Three witches all together

5) Ten 20c coins and six 50c coins

6) 59 sweets

Why? 

An approach is to eliminate possibilities, starting with multiples of 5. If it is divided by 5 it has a remainder of 4. Therefore it is a multiple of 5 plus 4.

It cannot be an even number so multiples of 10 don’t need to be checked.

So it is possibly: 9,19,29,39,49,59,69,79,89,99

9,39,69,99 are all multiples of 3, so can be eliminated.

Try dividing the remaining possibilities by 4 to see if they have a remainder of 3:

19 – remainder 3,
29 – remainder 1,
49 – remainder 1
59 – remainder 3
79 – remainder 3
89 – remainder 1

Three possibilities left: 19,59,79

Divide by 3, see if they have a remainder of 2:

19 – remainder 1
59 – remainder 2
79 – remainder 1

That leaves 59 as the only possible value.

7) Make two vertical cuts at right angles to each other to get 4 equal portions. Finally, move halfway down the outside and make a cut horizontally to result in 8 portions.

8) They took an apple out of the Red and Green box. If it is red, they know that box must
contain the green apples (as it can’t contain red and green). Then the Red labelled box
cannot contain red, so must contain green and red. The Green labelled box must then
contain the red.