Largest Product

Using all the digits from 1 to 7, what two numbers have the largest product? For example, 1234 x 567 = 699678 but you can do much better than that.

742 x 6531 = 4,846,002.

A similar problem can be found in L.A. Graham’s Ingenious Mathematical Problems and Methods with a range of 1 to 9, but the principle remains the same – the numbers with the smallest difference produce the largest product. You start out with the highest two digits, 7 and 6, then attach 5 and 4, putting the smaller of the two digits with the larger number, giving you 74 and 65. The next two highest digits are 3 and 2, giving you 742 and 653. Finally, you add the 1 to the lower number. Page 80 has the details of that solution.

Posted in Brain Teasers

The Odd One Out

Which is the odd one out and why?

A. Cassius
B. Cassia
C. Casca

B. Cassia is a tropical tree; Cassius and Casca were conspirators against Julius Caesar.

Posted in Brain Teasers

Next Month In the Sequence

What month comes next in this sequence?
July June March May ???

November, the next month in alphabetical order starting with July.

Posted in Brain Teasers

A Hundred Legs But Can’t Stand

I have a hundred legs, but cannot stand.
I have a long neck, but no head.
I cannot see, yet I help keep your house neat and tidy.

A broom.

Posted in Riddles

Ten Times Two is 0218

10 × 2 = 0218
20 × 2 = 1421
30 × 2 = 1632
40 × 2 = ?

2840.

This makes the first column the start of the Fibonacci series: 0, 1, 1, 2.
The second column is the even numbers: 2, 4, 6, 8
The third column is counting up by ones: 1, 2, 3, 4
And the last column is the answer in the first row in reverse: 8, 1, 2, 0.

Don’t ask what 50 × 2 equals. I have no idea. :)

Thanks to Jim for helping with the solution.

Posted in Brain Teasers
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Gain and Lose the Most

Some are quick to take it.
Others must be coaxed.
Those who choose to take it
gain and lose the most.

Risk.

By Sef Daystrom

Posted in Riddles

Special Two Letter Combinations

What do these three letter combinations have in common?

DE
HI
MN

Hint: These combinations don’t have it in common.

AK
IN
WY

They are the only three US state abbreviations whose two letters are next to each other in the alphabet.

DE – Delaware
HI – Hawaii
MN – Minnesota

Posted in Brain Teasers

Enjoyed By Some, Despised By Others

I am enjoyed by some, despised by others. Some take me for granted, some treasure me like a gift. I last forever, unless you break me first.

Marriage.

Posted in Riddles

esroh gnidir

What does this represent?

esroh gnidir

Horse back riding. The words are horse and riding spelled backwards.

Posted in Brain Teasers

Black We Are And Much Admired

Black we are and much admired,
men seek us if they are tired,
We tire the horse, comfort man,
guess this riddle if you can.

Coal.

Posted in Riddles