# Some .oints and numbers

What short word is missing in the puzzle below? Explain your reasoning.

                .6    .2.3   .1.4    .1.1.3   .2.4    .3   .8    .9   .3    .1.1   .1.4   .3    .8    .1.1.3   .1.1.1   .2.4    .1.2.2    .8   .1.2    .1.2.2    .2.2    .8     0.   .1.1.3    .2.4    .1.2.2     .8   .2.4    .1.4


No knowledge required except some trivial.

• Is the big space at the beginning intended? Commented Jan 25 at 18:28
• @RonchenLuo No, not intended Commented Jan 25 at 19:50

The missing word is:

DAY

The dot ...

... represents p, which can be seen from the title, where the word "points" is rendered as ".oints". We can also see that numbers in a "word" are increasing, that numbers can occur more than once and that if there are several numbers in a "word", they are small, most frequently ones and twos. And the dot (or p) comes before all digits, but after the zero.

So what do the numbers mean?

Now imagine the numbers as indices: p6 , p2 p3 , p1 p4 , ...

Here, pn represents the n-th prime number:

.1 .2 .3 .4 .5 .6 .7 .8 .9
 2 3 5 7 11 13 17 19 23

Juxtaposition of variables means multiplication, so the first three terms are:

p6 = 13
p2 p3 = 3 · 5 = 15
p1 p4 = 2 · 7 = 14

Can you see where this is going?

Each term ...

... represents a letter: The product of prime numbers is the index of a letter in the alphabet: 13, 15, 14 represents the letters M, O and N.

The whole expression resolves to:

MON TUES WEDNES THURS FRI SATUR SUN

These are, of course, the days of the week with the small word DAY missing from each.

(The term 0. represents the letter A with index 1, which cannot be represented as a product of prime numbers. Perhaps 0 p means "no prime". Anyway, that's a special case.)

• That's the word, great job! Commented Jan 25 at 20:50