think again!

How many four digit numbers are there where the digits are ascending from left to right?

- I see you got a new calculator. Congratulations!
- Thank you, but it is no good!
- How come?
- I set it to degree mode, typed in a lot of 5s, pressed 1/x, followed by sin.
- And?
- How can I believe the result?

Problem source: Division by zero.

What is less wasteful: to cut out a circle from a square, or a square from a circle?

Problem source: MathsChallenge.net.

Ice cream cones come in three cone types: plain, sugar, and waffle, and in fourteen flavours: vanilla, chocolate, rocky road, mint chocolate chip, strawberry, pralines and cream, bubble gum, butter pecan, mud pie, peanut butter crunch, almond fudge, coffee, chocolate chip, and banana royale.

You want to buy a two-scoop cone. How many are there to choose from?

Warning: only 16% of the submitted answers were correct (297 out of 1841) when it was presented as Problem of the Week at Columbus State University.

Find four consecutive natural numbers. When you have found them, ask them to be quiet so you can multiply them. If the answer is a square number, jump up and down in joy.

Problem source: Wisconsin Mathematics Science & Engineering Talent Search.

If the solid lines mean multiply and the dotted ones means add, can you add numbers in the empty circles? How do you do it?

Problem source: The Number Warrior. The diagram is borrowed from the same source.

- What are you reading?
- You will like this. The author says the soft maximum of 1 and 2 is 2.31.
- Is he still loose or in an asylum?
- I think he is an assistant professor.
- Why will you never answer my questions?
- On the other hand, the soft maximum of 10 and 20 is 20.000005.
- That is better, but every kid under 5 knows the answer is 20.
- You need to work on your listening skills. The maximum, what the author calls the hard maximum is 20, but the soft maximum is 20.000005.
- What is soft maximum? I thought it was the bigger number of the two.
- The soft maximum of two numbers a and b is sm(a,b) =  ln(e^a + e^b).
- You mean the natural logarithm and its inverse function? I thought this blog could be read by anyone!?

- Another definition is sm(a,b,k) = ln(e^(ka) + e^(kb))/k.
- Light, can we have some light please!?
- sm(1,2,1) = 2.31 while sm(1,2,10) =  20.000005.
- So when k increases the soft maximum approaches the hard maximum?
- That’s today’s question.

Problem source: The blog of John D Cook.

When I was in town the other day I accidentally found this graph in the gutter. It was very unhappy as it had forgotten who it was. The graph also told me it used to be most happy for a number between 2.5 and 3, but could not remember the exact number.

Can you bring identity and happiness to this graph? The phone lines are open and operators are standing by for your solution. Please call GRAPH-HELPLINE.

The photo of the graph was taken with the free software Maxima.

On the dy/dan blog there is a video with a question. Can you answer it?

- Why! Do you look depressed!
- I have every reason to.
- I have only seen you once like this. When the doctor at the hospital said ‘You are going home today’ and you misheard it as ‘You are going home to die.’
- The doctor called me again today.
- Are you sure it was today?
- Morbidly funny!
- What did he say?
- That I have tested positive for a deadly disease.
- Did he say which one?
- Does it matter?
- What more did he say?
- The test is 99% reliable.
- What does that mean?
- That if you have the disease the test will reveal it in 99% of the cases.
- And if you don’t?
- Then the test will say you have the disease in 1% of the cases.
- All these talk about percentages has made me thirsty. Let’s go and find a bar.
- I am dying and all you can think of is booze!?
- When we are both drunk maybe we’ll see the world in a brighter light.

Problem source: http://thinkzone.wlonk.com/ by Keith Enevoldsen.