# A haphazard problem selection

This time round, some more or less randomly chosen problems. Each one needs a different approach. On request, I may be persuaded to provide my attempt at an answer 🙂

**1. Each person at a dinner party for 10 ‘clinks’ their glass with all other guests. How many clinks?**

Not too hard if you count right.

**2. If you fold a (humungous) piece of paper in half 50 times, how thick would the pile be? 1cm, 1m, 1km, 1,000km, 1,000,000km…?**

A relatively simple, if surprising, calculation.

**3. What is the smallest integer which returns “did not match any documents” on a Google search?**

Much more interestingly, what search method did you use?

Testing one by one is obviously not practical for numbers this big.

And how close do you think you are to the actual answer?

There must be one, even if it changes from day to day.

**4. How many (a) squares and (b) rectangles (of any integer size) on a chessboard?**

I may be stealing some Year 8 maths teachers’ thunder here. In any case, the key is to find a good method of counting. Just listing them is almost impossibly tricky and tedious. But an exact answer is there in both cases.

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P.S. I was hoping to have a summary of my cube calendar solution by now, but the scope has expanded, and I am now doing it for lots of languages – about 40 so far. I hope to report back next week.