Another Not-So-Straightforward Math Puzzle


The other day, I posted a peculiar math puzzle here. Some readers of Learn Fun Facts seem to like this type of puzzle. So, here’s another one, also from John Jackson’s Rational Amusements from Winter Evenings (1821):

One third of twelve, if you divide,
By just one fifth of seven,
The true result (it has been tried,)
Exactly is eleven.


Similar to the first Not-So-Straightforward Math Puzzle, the solution also involved wordplay, Roman numerals, and simple arithmetic.

“One third of twelve” here is equal to 55. Why?

The word TWELVE consists of six letters. Therefore, one-third of TWELVE is 2 and in this case, we choose LV, the Roman numeral of 55.

The same principle applies to the “one fifth” of seven.

One-fifth of SEVEN is 1 and only the letter V (Roman numeral of 5) is a Roman numeral so that’s what we select.

Thus, one-third of TWELVE divided by one-fifth of SEVEN is equal to 11.

55 ÷ 5 = 11

Just for fun, here’s one more similar puzzle. This is from The Ladies’ Diary, Vol. 66 (1769):

Four things I saw, but what they were,
I beg, dear ladies, you’ll declare;
And though they were but four exact,
Thirteen they were full as compact;
I cut off half, and then could find,
Exactly eight were left behind:
What seems more strange tho’ very sure,
These eight remaining, were but four.

I won’t provide the solution for this one so, try to figure it out yourself. This should be easier than the previous ones as you already had some practice.

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My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. You can find me on Twitter` and Facebook. My email is

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