Laying Coins on a Table

Last Problem:

What do the red letters have in common?

What do the black letters have in common?

ACTBYK

MDUEW

Answer:

The red letters are the capital letters in the alphabet that have only vertical symmetry. The black letters are the capitals that have only horizontal symmetry.

Today’s Challenge:

Two players take turns placing identical coins on a perfectly round table. The first player who cannot put a coin on the table without overlapping an existing coin loses.

Devise a strategy so that one of the players will always win, no matter how large the table is.

What do these Letters Have in Common?

Last Problem:

Pick any two people out of all the persons living in the United States. If you wanted to link those two persons by a chain of acquaintances (such as a friend of a friend of a friend …), how many people or connections would you need to make on average?

Answer:

The usual answer to this question is that it would take about 100 people to make a connection. Research shows however that any two strangers in the United States can be linked by a chain of intermediate acquaintances only five to six people long.

This problem is otherwise known as the “small world” problem. Chains of acquaintances have always been important, but revolutions in communication over the past decade mean today that people are connected to one another through a few connections to virtually every person on the planet.

Today’s Problem:

What do the red letters have in common?

What do the black letters have in common?

ACTBYK

MDUEW

Small World Problem

Last Problem:

You are celebrating today the birthday of your two year old niece. Her birthday cake has two candles proudly place on top. When your niece attempts to blow out the two candles, she blows between them (instead of blowing them out). What happens to the flame of the candles? Do the flames move outward, inward or simply flicker?

Answer:

The stream of air creates a low pressure zone which draws the flames closer together.

Today’s Problem:

Pick any two people out of all the persons living in the United States. If you wanted to link those two persons by a chain of acquaintances (such as a friend of a friend of a friend …), how many people or connections would you need to make on average?

Birthday Cake Candles

Yesterday’s Problem:

Fill a glass with water completely up to the rim. Then slip a penny into the glass. The water will not overflow with just one additional penny inside. Approximately how many pennies can you slip into the glass before the water spills over the edge?

Try it out. See what you get. This is something fun to do on New Year’s Day, eh?

Answer:

The precise answer will vary of course depending on circumstances, but you can put as many as 52 pennies into the glass before it overflows.

Water has a very high surface tension. It behaves much like flexible skin which pills inward and always resists breaking.

A glass of water can develop a huge bulge before it flows over the edge of the glass. Surface tension can also support the weight of light objects. For example, if you place a razor blade flat against the surface of the water, the razor blade will actually float on top of the water even though you would expect it to sink down to the bottom because of its weight.

Surface tension of the water holds up the razor blade. It is certainly not held up by the buoyancy of the razor blade which is very dense.

How many pennies did you successfully put into your glass?

Today’s Problem:

You are celebrating today the birthday of your two year old niece. Her birthday cake has two candles proudly place on top. When your niece attempts to blow out the two candles, she blows between them (instead of blowing them out). What happens to the flame of the candles? Do the flames move outward, inward or simply flicker?

Pennies in a Water Glass

Previous Problem:

This problem will take a few days to solve, so it is perfect for the holidays when you are looking for fun activities.

Consider the numbers 1 to 40, inclusive. Imagine trying to express each of those numbers as a combination of other numbers that are added or subtracted together – for example, 3 can be 1+2 or it can be 4-1.

Identify four numbers that, either singly or combination with some or all the other three numbers, can express every number from 1 to 40. In each combination however, any given number can appear only once – for example, 5 + 5 is not allowed. To check your answer fill in the table below with the various combinations.

1 =

2=

3=

4=

5=

6=

7=

8=

9=

10=

11=

12=

13=

14=

15=

16=

17=

18=

19=

20=

21=

22=

23=

24=

25=

26=

27=

28=

29=

30=

31=

32=

33=

34=

35=

36=

37=

38=

39=

40=

Answer:

The numbers are 1,3,9 and 27. This problem is a good exercise in getting the maximum work from a minimal number of elements (or the maximum relief from Parkinson’s symptoms from the fewest number of therapies!)

1 =1

2=3-1

3=3

4=3+1

5=9-3-1

6=9-3

7=9-3+1

8=9-1

9=9

10=9+1

11=9+3-1

12=9+3

13=9+3+1

14=27-9-3-1

15=27-9-3

16=27-9-3+1

17=27-9-1

18=27-9

19=27-9+1

20=27-9+3-1

21=27-9+3

22=27-9+3+1

23=27-3-1

24=27-3

25=27-3+1

26=27-1

27=27

28=27+1

29=27+3-1

30=27+3

31=27+3+1

32=27+9-3-1

33=27+9-3

34=27+9-3+1

35=27+9-1

36=27+9

37=27+9+1

38=27+9+3-1

39=27+9+3

40=27+9+3+1

Today’s Problem:

Fill a glass with water completely up to the rim. Then slip a penny into the glass. The water will not overflow with just one additional penny inside. Approximately how many pennies can you slip into the glass before the water spills over the edge?

 

Four to Make Forty

Last Question:

Unscramble the letters

t-r-e-b-e

to describe a french hat

Answer:

b-e-r-e-t

This week’s Challenge:

This problem will take a few days to solve, so it is perfect for the holidays when you are looking for fun activities. I will post the answer on New Year’s day.

Consider the numbers 1 to 40, inclusive. Imagine trying to express each of those numbers as a combination of other numbers that are added or subtracted together – for example, 3 can be 1+2 or it can be 4-1.

Identify four numbers that, either singly or combination with some or all the other three numbers, can express every number from 1 to 40. In each combination however, any given number can appear only once – for example, 5 + 5 is not allowed. To check your answer fill in the table below with the various combinations.

1 =

2=

3=

4=

5=

6=

7=

8=

9=

10=

11=

12=

13=

14=

15=

16=

17=

18=

19=

20=

21=

22=

23=

24=

25=

26=

27=

28=

29=

30=

31=

32=

33=

34=

35=

36=

37=

38=

39=

40=