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Blast into Math! Pure mathematics: the proof of the pudding is in the eating

• * Problems: The problems with a ∗ may be more challenging. Please take your time with
these problems and enjoy the adventure of problem solving! If you have worked hard and
earned a hint according to The Hint Rule, you may read the hint and then continue working
on the problem. If you are still stuck, please take a break from mathematics and return to
the problem several hours or a day or two later. Keep a positive attitude and remember that
mathematicians around the world are also struggling to solve problems; you are working

within the international mathematics community. We are all cheering for you and your
efforts!
• Hint for # 9: In any good problem you will need to use every hypothesis. In this problem
you will need to use the fact that one door always tells the truth and the fact that the other
door always lies. You don’t know which is which, and you can only ask one door. This means
that you need a question which you can ask one door which involves both doors at the same
time. Somehow you want to use the truth-telling door to filter the lie from the lie-telling

door. This is a * problem, but don’t let that discourage you! If you are reading this, then you
have worked hard and earned a hint, and the problem is steadfast in your brain. You should
stop thinking about it for a while and go do something other than mathematics. If you stop
thinking about the problem and come back to it later, you may suddenly have a new idea!
Please believe in yourself, and give yourself the chance to have such moments. Give yourself
a whole month, and if you still haven’t come up with a solution to this problem then you
may watch the film.
• A comment on # 10: The ending ♥ is to congratulate you the reader! After working
diligently through each proof ♥ symbolizes an enthusiastic round of applause for your

efforts and a freshly baked homemade cookie.

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