Given:

1. Two of them play football, two play basketball and two play hockey.
2. The friend who does not play hockey does not play basketball as well.
3. The friend who does not play football does not play hockey.

From the statements 2 & 3, it follows that one of the friends does not play any of the three sports, because, as per Statement 3, there is one person who does not play football, and the same person does not play hockey either. But, since (s)he does not play hockey, by statement 2, should not play basketball either, which means that, that particular friend does not play any of the three sports. Being so, BOTH the remaining friends must play ALL three items to satisfy the first condition. Since none of the name – sport combination is given, the two playing and one non-player friends can be any of the three.

The blind beggar is the sister of the brother who died.

707

Sum of Digits: 7 + 0 + 7 = 14
Square: 707^2 = 4,99,849

It is specified that:

(1) Each digit represents a digit.
(2) The similar letters carry the same integer value

It does NOT say that distinct letters must correspond to distinct digits. Hence, three possible solutions are there.

Possible answers:

1. T = 1, W = 3, O = 0; H = 6, R = 9 and E = 0, so that TWO = 130, THREE = 16900
2. T = 1, W = 4, O = 0; H = 9, R = 6 and E = 0, so that TWO = 140, THREE = 19600
and
3. T = 1, W = 3, O = 8; H = 9, R = 0 and E = 4, so that TWO = 138, THREE = 19044

If the additional condition that distinct letters must correspond to distinct digits, only the third  solution is valid (because in the other solutions, lettes O and E represent the same digit 0.)

False.

It is not necessary that “some Marigold are used to make colours”.  A scenario as shown is possible.

20

The question says “Use three 9s in a mathematical expression…” It does NOT say that you shouldn’t use any other digits / numbers.  🙂
Being so, there are an infinite number of possible, valid answers, such as ‘1000 – 999’.

One in a Million

The question is “will you be able to win a thousand apples”. So, my answer is YES. The question does NOT ask to explain HOW I can win.

If asked, I would pack the apples as below:

47632

Only number divisible by 4.

36119

Only number that contain same digit repeating consecutively

More answers may be possible, based on different sets of logic applied.