Riddles and Brain Teasers

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.

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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.

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

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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 ???

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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.

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A broom.

Posted in Riddles

Ten Times Two is 0218

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

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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.

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

Tagged with Series