Below you will find some well known eight-letter words, with only their endings remaining. Can you determine the words?

.....YEE

.....EGY

.....IGM

.....LSE

.....COM

.....BET

.....LEL

.....DEE

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A maths problem, which was originally produced for 14-year-old students in Singapore, has confused adults worldwide. To be fair, it was written for the Singapore and Asian Schools Math Olympiads - a competition reserved for highly intelligent 14-year-olds, but an adult should still be able to solve it, right?

Question

Albert and Bernard just become friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:

May 15, May 16, May 19

June 17, June 18

July 14, July 16

August 14, August 15, August 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.

Bernard: At first I don't know when Cheryl's birthday is, but I know now.

Albert: Then I also know when Cheryl's birthday is.

So when is Cheryl's birthday?

The key to the whole problem is realising why at the start of the puzzle Albert knows that Bernard does not know her birthday. Anyway here's my attempt at an explanation.

1. For Bernard not to know the date, the day must be one of those that appears more than once i.e. it cannot be 18 or 19.

2. For Albert to know that Bernard cannot know the date he must know that the number given to Bernard was not 18 or 19. The only way he can be sure this is not the case is if the month given to him was not May or June.

3. Bernard knows after Albert's statement that the month must be July or August. If he then knows the exact date then the day cannot be 14 as there is one in each month so the date must be July 16, August 15 or August 17.

4. After Bernard's statement, Albert also knows the date must be one of those three and for him to know the exact date he must have been told the month was July, since if it was August he would still have two possible choices.

5. The date is July 16