Judging from the responses you had a lot of fun with the last math puzzles. The solutions and new challenges are here. The names of the winners are included in the HALL OF FAME. Let us pay homage to these keen mathematical minds. Join us in honoring and congratulating our champions. Thank you for submitting your entries. Remember to add this interesting page to your bookmarks and check back for new puzzles.

CONGRATULATIONS

Mathematicians Hall of Fame

These are the persons who have demonstrated mathematical expertise.

Graeme Lindridge, Tasmania, Australia

Cecil Malherbe, Ninapark, RSA (South Africa)

Joe Keilin of Mendham, New Jersey (twice)

Christiane Siemer of Blaustein, Germany

Malika Roy of Fort Lee, New Jersey

David A. Mote of Reading, Pennsylvania

Ken Lenkiewicz of Incomplete Address

Miriam ? of Yonkers, New York

Scroll Slowly to delay seeing the answers ( if you have not seen these puzzles before and you want to see if you would have made it to the HALL OF FAME).

1. Exactly 63.41463414 % of the people asked if they used a certain product, replied "Yes".

What is the smallest number of people who could have been asked the question?

2. Something = nothing?

Let S= 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + . . . . . . .

Then taking 1/2 of each term

1/2 S= 1/4 + 1/6 + 1/8 + 1/10 + 1/12 + 1/14 + . . . . . . .

Subtract 1/2 S from S, the result is

1/2 S= 1/2 + 1/3 + 1/5 + 1/7 + 1/9 + 1/11 + . . . . . . . .

Subtracting the first expression for

1/2 S from the second expression for

1/2 S, we get

1/2 + (1/3 - 1/4) + (1/5 - 1/6) + . . . . = 0

Or 1/2 + 1/12 + 1/30 + 1/56 + 1/90 = 0

Proving that something equals nothing.

Do you believe it? Or, is there a reason? Explain.

Solution #1

As a fraction, 63.41463414%=63414/99999=7046/11111=26/41
41 people were asked, 26 replied yes

Solution #2

The series in the first line does not have a finite sum. If you add enough terms you can make it as large as you please. Therefore, it is a mistake to call its sum S, and you certainly can not start working out 1/2 S.

Challenge #1

Each of these true statements refers to seven out of eight of the living members of the Jones and King families, either by their personal name or by their relationship to another member.
1. John's wife's sister's husband's mother's son is Peter's cousin's father.
2. Sally's grand-daughter's cousin's father's sister-in-law is Gregory's son-in-law's wife.

Question

If Anita has no children, what relationship is she to Mike? (Yes, all the information is here. There are two possible solutions.)

Challenge #2

Find the sum of this series

1/2 + 2/4 + 3/8 + 4/16 + 5/ 32 + . . . =

Challenge #3

Find the sum of this series 1/2 + 3/4 + 5/8 + 7/16 + 9/32 + . . . =

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