# What number is that ? Asks Grandpa

"So here is a number between 1 and 60" Says Grandpa

"If you take its WORD anagram and subtract this number you will get

Anagram of the number - number > 5

What is that number"?

"So it is the anagram of the spelling of the number?" I asked

"Yes, son. Think"

Post script

I see a lot of Fractions as answers. There is a simple integer solution. No Fraction.

• Noting the absence of the 'language' tag, I'm guessing Grandpa's only interested in English words for numbers?
– Stiv
May 13 '20 at 13:15
• That is right @Stiv
– DrD
May 13 '20 at 13:27
• Considering the accepted answer, you can't really put that into a mathematical equation. You already mostly wrote it out in words (which would loosen up the allowable inputs a bit), so I would suggest just finishing that sentence, i.e. "... you will get a number greater than 5" and removing the equation. May 14 '20 at 13:26
• This is quite brilliant, why not ask a generalization to other languages? (e.g. What is the smallest number in each language L having the property that its anagram is also (objectively) a legitimate number or numerical quantity in that language?)
– smci
May 14 '20 at 17:36
• – smci
May 14 '20 at 18:03

Grandpa is thinking of

45

because

FORTY-FIVE

anagrams to

OVER FIFTY

and

OVER FIFTY minus FORTY-FIVE yields over five.

• This sounds right. I like it. +1 May 13 '20 at 20:08
• I agree with MacGyver88, this really explains the lower bound. +1
– Tom
May 13 '20 at 20:35
• @Tom abj pna lbh thrff gur nafjre gb gur cerivbhf dhrfgvba: Fnl zr bhg ybhq V jvyy trg fgebatre?
– DrD
May 13 '20 at 22:42
• @DEEM, oh I see, but not all the answers, I may post a try!
– Tom
May 14 '20 at 5:11

NB This answer was given when the first line of the puzzle read: "So here is a number below 60" Says Grandpa - since then a further stipulation has been added to restrict the number further to 'between 1 and 60'...

I note that Grandpa hasn't specified that the number must be:

greater than 0 - just that it has to be "below 60".

To this end, I propose that Grandpa might be thinking of:

MINUS SEVENTY-SIX (-76)

Its anagram is then:

MINUS SIXTY-SEVEN (-67)

and the calculation works out as:

-67 - (-76) = -67 + 76 = 9

which is indeed larger than 5...!

• I am sorry @Stiv. I should have written that it is between 0 to 60. MY BAD
– DrD
May 13 '20 at 14:19
• @DEEM Aw, that's a shame - I thought I had it! :)
– Stiv
May 13 '20 at 14:20
• MY apology. Not thinking straight. Your way it could be -79 and -69 also right?
– DrD
May 13 '20 at 14:22
• @DEEM Not quite - the first digit has to be the larger of the two to end up with a difference greater than positive 5 when the number is taken from its anagram. My way, it could be any of -76, -86, -87, -96, -97 or -98 (if we restrict ourselves to just two-digit negative numbers) - I chose -76 as the largest of all the possibilities.
– Stiv
May 13 '20 at 14:27
• Actually, the ones involving an 8 wouldn't work, since you only add a 'y' when it's in the tens place, and the other digits add a "ty", so they won't anagram properly. May 14 '20 at 14:53

Ok thinking outside the box...

The number could be

One

Since

Eon - One > 5 Since an eon is a really big number (can be 1 Billion or just a really impossibly long measure of time) that minus 1 is always greater than 5

• Wow. Great out of the box thinking @Bee. +1 Grandpa had another number in mind
– DrD
May 13 '20 at 13:53

Oh boy, here I go swiping again:

The number is

Fifty-sevenths, $$\frac{50}{7}$$, and its anagram is seventy-fifths, $$\frac{70}{5}$$.

The difference is

$$\frac{70}{5}-\frac{50}{7} = \frac{490-250}{35} = \frac{240}{35}= \frac{48}{7} = 6 \frac{6}{7} > 5$$.

Second Try

I’m going to use

an incorrect (obsolete) spelling of forty, namely fourty, to get fourty-six and sixty-four (64-46=18).....

• Wow. OK. But there is a simple integer number @El-Guest
– DrD
May 13 '20 at 15:52
• Outside of using an incorrect spelling for forty (ie. fourty), I’m not seeing any integers with anagrams... @DEEM May 13 '20 at 16:01
• Boy you are so close @El Guest
– DrD
May 13 '20 at 16:35
• @DEEM is my second attempt correct? May 13 '20 at 16:54
• Thank goodness, that would’ve been a copout of an answer May 13 '20 at 17:56

Perhaps the integer between 1 and 60 is

50, or as Grandpa calls it, three hundred and fifty sevenths

the anagram of the number - number > 5

three hundred and seventy fifths - 50 = 74 - 50 = 24

I upvoted El-Guest's answer and it may have been sniped !

• it took me a while, I was thinking that rot13(guerr uhaqerq naq svsgl friragu jnf guerr uhaqerq naq (svsgl friragu)) May 13 '20 at 20:59
• @melfnt, NP - I hoped there being no hyphen between the last two words made this ok. Still, serves me right trying to snipe, shoover's answer is better.
– Tom
May 13 '20 at 21:18

46 and 64

Fourty Six and Sixty Four

64 - 46 = 18 > 5

• Think I ninjaed you if this is correct, but nice guess! May 13 '20 at 16:57
• I think you were just pipped to this suggestion by @El-Guest by about 5 minutes - bad luck! But welcome to Puzzling :)
– Stiv
May 13 '20 at 16:58
• Yes. It was based on @El-Guest's finding. No denying. :) May 13 '20 at 17:00
• Spelling is important! Forty is the correct spelling
– DrD
May 13 '20 at 17:49
• @DEEM..So this is not the correct answer?? May 14 '20 at 6:53

I dont know if this qualifies for anagram, still the difference is too low

the number could be $$\frac{50}6$$ with anagram `sixty fifth'. The difference is $$\frac{60}5-\frac{50}6 = 3.66..$$'

• But is it > 5??
– DrD
May 13 '20 at 15:17