The riddle, solved

Which Roman numerals multiply to 35?

The short answer, then the reasoning, laid out clearly.

V × VII
5 multiplied by 7 equals 35
The factor pairs of 35
I × XXXV1 × 35, the trivial pair
V × VII5 × 7, the answer

35 is the product of two primes, 5 and 7, so those are its only factors above one. In Roman numerals that is V and VII.

The answer

The two Roman numerals that multiply to 35 are V and VII. V is 5, VII is 7, and 5 multiplied by 7 is 35. That is the whole puzzle, and it is the only sensible pair that works.

Why V and VII is the only answer

To find which numbers multiply to 35, you factor it. A factor pair is two whole numbers that multiply to give the target. For 35 the factor pairs are 1 and 35, and 5 and 7. That is all of them, because 35 is the product of two prime numbers, 5 and 7, and nothing else divides into it evenly.

The pair 1 and 35 is the trivial one: multiplying anything by 1 leaves it unchanged, so I times XXXV technically reaches 35 but is not what the riddle is after. That leaves 5 and 7, which as Roman numerals are V and VII. Since both can be written as numerals and their product is 35, they are the intended and unique answer.

Factor check: 35 = 5 × 7. In Roman numerals, 5 is V and 7 is VII, so V × VII = 35.

Where this question comes from

It is Rule 9 of The Password Game, the browser game by Neal Agarwal in which you build a single password that has to satisfy every rule at once while the rules keep coming. Rule 9 reads: the Roman numerals in your password should multiply to 35. The number is fixed in the game, which is why you see this exact question and never a "multiply to 50" or "multiply to 100" version of it.

The puzzle lands because it looks harder than it is. Dressing a simple multiplication in Roman numerals makes people pause, and the phrasing hides that you are really just factoring 35. Once you see that 35 breaks into 5 and 7, the numeral layer falls away.

Getting it to actually go green

Knowing the answer is V and VII is not always enough to clear the rule, because the game reads your whole password, not just the part you meant as an answer. Three things catch people out:

The rule before this one, Rule 7, include a Roman numeral, is where to solve this cheaply: answer it with V and VII rather than a lone X and Rule 9 is green before it appears. For the chart and the later rules that quietly break your numerals, see Roman numerals in The Password Game.

Frequently asked questions

Which two Roman numerals multiply to 35?

V and VII. In numbers that is 5 multiplied by 7, which equals 35. Those are the only two Roman numerals that multiply together to give 35.

Why is the answer V and VII and not something else?

35 has only one pair of factors greater than one: 5 and 7 (since 35 = 5 x 7). Both 5 and 7 can be written as Roman numerals, V and VII, so that pair is the unique answer.

Is 35 in Roman numerals the same as the answer?

No. 35 itself is written XXXV. The riddle is not asking for 35, it is asking which two numerals you multiply to reach 35, and that is V times VII.

Could I use I in the answer?

Only trivially. I is 1, and multiplying by 1 changes nothing, so I times XXXV also gives 35. The intended, non-trivial answer is V and VII.

What is 35 in Roman numerals?

35 in Roman numerals is XXXV (XXX for 30 plus V for 5). That is the number 35 itself, which is different from the riddle: the riddle asks which two numerals multiply to 35, and that is V times VII.

What do V and VII stand for?

V is 5 and VII is 7. Multiplied together they give 35, which is written XXXV in Roman numerals.

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