# Creating an easy mathematical puzzle that leads to the number 60 [closed]

For my fathers 60th birthday I'd like to paint a fun equation or preferably an easy mathematical puzzle on a poster that I will hang up for him.
It should lead to the number 60 and be easy, so that someone with very limited mathematical knowledge can solve it(No complicated integrals etc.).
I sadly have super limited knowledge and creativity when it comes to puzzles, so any input would be appreciated. Can anyone suggest a puzzle or give some tips on how to create one?

• It would help if you could make more clear what you mean by "very limited": Just plain arithmetic, or could we add factorials, exponentiation, trigonometry, logarithms ...? – KeyboardWielder Jun 17 '16 at 18:38
• What languages may be used? Wordplay could add to the fun, as could Roman numerals and other counting systems. A 30th birthday cake for a Latin and mathematics enthusiast had: FeliXXX – humn Jun 17 '16 at 19:03
• I don't suppose is nane is aLeX :) – Jasen Jun 18 '16 at 6:22

I don't know how simple you want it, but here's some suggestions:

$3*4*5$

$10+11+12+13+14$

$5!/2$ -- do you think he'll understand the mathematical meaning of '!'?

Draw an equilateral triangle (mark the sides as being equal). Mark one of the angles $x$ and ask "what is $x$?".

• Could be a 30-60-90 right triangle with arrows to each angle, saying "You are here?" – humn Jun 17 '16 at 22:12
• @humn Not sure that that makes the point. If the right-angle were marked as such, and the hypotenuse with $2x$ and the short leg with $x$, that'd do it, but that makes it look even more like a geometry exercise. – Rosie F Jun 18 '16 at 5:56
• 5!/2! would be more symmetrical – Jasen Jun 18 '16 at 6:17

Visual impact comes for free if you ask  to count  how many vertices (or carbon atoms) are on a truncated icosahedron (or C60 molecule$\small\raise2mu/$Buckminsterfullerene$\small\raise2mu/$bucky-ball or football$\small\raise2mu/$soccerball):

(You could even use an actual ball instead of a picture.)

Lighthearted variations:

• With a football$\small\raise2mu/$soccerball: “If you can find a vertex for each of your birthdays, have a ball!”

• “Show that a truncated dodecahedron (or bucky-ball$\small\raise2mu/$football$\small\raise2mu/$soccerball) has a prime number of vertices (or carbon molecules).” When the birthday boy answers, “there seem to be 60 vertices$\small\raise2mu/$atoms but 60 is not a prime number,” you can reply, “it is now, thanks to you!”

• Variation for a question to accompany a football/soccerball: "If you can find a vertex for each of your birthdays, have a ball!" – humn Jun 17 '16 at 19:51
• This is a really good one, actually. A surprising number of people would have difficulty accurately counting the vertices on a soccer ball. This would even make a fantastic 5-minute introduction to Combinatorics (counting). – Wildcard Jun 18 '16 at 5:13
• Indeed indeed, asking how many vertices (or carbon atoms) is much more interesting and potentially less tedious, perhaps also more considerate, than asking to count those birthdays one by one. Think I'll edit that into the idea/answer. – humn Jun 18 '16 at 7:13

Here's one from me, which is based on another puzzle of mine called The Magic Stick, and the fact that 60 is the smallest number that's divisible by the first six natural numbers:

Your grandson (or granddaughter, depending on whether you have kids and what they are) is playing with a small pile of centimeter cubes, stringing them up into long sticks.

First, he (assume he could be she in the rest of the question) arranges them into one big stick, which he holds in his hands. Then, he splits the stick into two equal pieces.

Then he puts it back together again and splits it into three equal pieces. He repeats for 4, 5, and 6 pieces, and each time he does this, each piece has the same equal number of cubes in it.

He tries for 7 and 8 as well, but those don't come out even. How many centimeters long is the one really long stick?

Now, this is a word problem, so it would probably go better on something like a birthday card. If you wanted to make it into a poster, you could have a stick of 60 cubes broken into 2, then 3, then 4, then 5, then 6 equal parts.

• This is also assuming that if you have kids, they're of the age at which they'd be playing with centimeter cubes. You could use a different example like sorting marbles into bags or action figures into boxes. – Joe Z. Jun 17 '16 at 17:59

Puzzle 1.

I am greater than $0$
I am less than $120$
I am divisible by $1,2,3,4,5,$ and $6$

Puzzle 2. (English only)

I am the largest integer which, spelled out, is five letters long

• Just out of curiosity, is it also the largest number (including non-integers) that can be spelled with 5 letters? – Dan Russell Jun 17 '16 at 18:30
• @DanRussell, I do believe it is. I've just spent a good while specifically thinking about this and pouring over pages of specially named numbers/trivia lists. Googol is the closest I can get but that has six letters. Some references: largest number possible up to x many letters (calculated) [dead link] webcache.googleusercontent.com/…, cool trivia [also now dead link]: webcache.googleusercontent.com/… – niemiro Jun 17 '16 at 20:50
• @niemiro Thanks for the followup. I couldn't think of anything offhand that would be greater, so the "integer" in Jonathan Allan's answer could probably be changed to "number". Another piece of trivia that will come in handy like two times during the rest of my life. – Dan Russell Jun 18 '16 at 3:35
• Puzzle 2 seems ambiguous to me. Cases could be made for 90 (the five letters being einty, with n repeated) or 5000 (MMMMM) – Peter Taylor Jun 18 '16 at 5:28
• @MarkPlotnick 90 is not divisible by 4 – Ovi Jun 18 '16 at 5:48

Here's a numerical one:

2^2 x 2^2 x 2^2 - 2^2

Here's a jokey one:

Happy 10th Birthday! (in base 60)

• It is confusing to have the exclamation mark behind the 10 – Dennis Jaheruddin Jun 18 '16 at 5:56
• "Happy 10th Birthday! (in base 60)"? – wizzwizz4 Jun 18 '16 at 7:15

Assuming that it's this month (2016-06), perhaps something along the lines of:

$(20 + \sqrt16)/6*15$

Knowing the exact date would help.

• Of course this idea can also be applied to his birthday. – Dennis Jaheruddin Jun 18 '16 at 5:54
• Exact date is 16.06 so this is actually very good – LionIsLoose Jun 18 '16 at 14:27

If you and your family are more of a "riddler" type, you might be able to get to something using the fact that there are 60 seconds to a minute and 60 minutes to an hour.

I'm, unfortunately, not good at creating riddles... ;c) (And English isn't my native language.)

Others have noted the divisibility of sixty, from that I developed this:

What happened when you were exactly half as old as today, and exactly one third as old as today and exactly one quarter as old as today and exactly one fifth as old as today and exactly one sixth as old as today ?

it's your birthday again, Happy Birthday!

• I think it's a little wordy, but -.(o.o).- – wizzwizz4 Jun 18 '16 at 15:55

In general, you could take any number puzzle that you like and tweak it a bit to come up with 60 (for example a 24 solution times 2.5). But here is what I could think off right now:

## Four fours: simple but thematic

4*4*4 - 4
4^4/4 - 4
44 + 4*4