This week we have an honoured guest – Alice. Yes, Alice from Alice in Wonderland!

Alice heard Tweedledum say: Yesterday we got a number of wine gums. We both got the same number, but we played a game which I won and then I had 5 times as many wine gums as Tweedledee. But when I gave him one of my wine gums, I had only 4 times as many wine gums as he had.

This week we have an honoured guest – Alice. Yes, Alice from Alice in Wonderland!

Alice heard Tweedledum say: Yesterday we got a number of wine gums. We both got the same number, but we played a game which I won and then I had 5 times as many wine gums as Tweedledee. But when I gave him one of my wine gums, I had only 4 times as many wine gums as he had.

1) How many wine gums did Tweedledee and Tweedledum have?

That’s strange, Alice said. Yesterday, I mean the day before I fell into this rabbit hole, I had been playing a game with my sister. We were playing for matches, and after the game I had 7 times as many matches as my sister. But when I gave her one of my matchsticks, I had only 6 times as many matches.

2) How many matches did Alice and her sister have?

I was telling the story above to a little girl called Alais. Alais thought for a moment, then told me: That is strange. Yesterday, the day before you told me this puzzle, I was playing a game with my little sister. After the game, I had 10 times as many gumdrops as she had. Of course I gave her one, and then I had exactly 9 times as many as she had.

3) Alais is obviously a very smart girl. I knew she had had some elementary algebra at school. She had obviously figured out that there are an infinite number of numbers with which this puzzle can be told. Can you explain why?

You can check your solution here

New puzzles are published at least twice a month on Fridays. Solutions are usually published after one or more weeks.