What number is that ? Asks Grandpa

Question

"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
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. — NotThatGuy, 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
Here's the Multiilanguage generalization of “What number is that? Asks Grandpa” — smci, May 14 '20 at 18:03
Thanks for asking @smic. I am thrilled with the answers to your question — DrD, May 14 '20 at 19:05

score 47 · Accepted Answer · answered May 13 '20 at 20:01

47

Grandpa is thinking of

45

because

FORTY-FIVE

anagrams to

OVER FIFTY

and

OVER FIFTY minus FORTY-FIVE yields over five.

answered May 13 '20 at 20:01

shoover

5,201
22
29

4

This sounds right. I like it. +1 – MacGyver88 May 13 '20 at 20:08
2

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 05:11

Stiv · Answer 2 · 2020-05-13T14:22:55.423

16

^{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...!

edited May 13 '20 at 14:22

answered May 13 '20 at 14:18

Stiv

140,467
11
495
752

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
2

@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
2

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. – Darrel Hoffman May 14 '20 at 14:53
@DarrelHoffman That's a fair point - so re my comment above, it would actually only be for -76, -96 and -97 in double digits. – Stiv May 14 '20 at 14:55

score 14 · Answer 3 · answered May 13 '20 at 13:30

14

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

answered May 13 '20 at 13:30

Gamora

654
3
12

4

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

El-Guest · Answer 4 · 2020-05-13T16:49:54.903

11

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).....

edited May 13 '20 at 16:49

answered May 13 '20 at 15:34

El-Guest

32,273
3
81
126

Wow. OK. But there is a simple integer number @El-Guest – DrD May 13 '20 at 15:52
1

Outside of using an incorrect spelling for forty (ie. fourty), I’m not seeing any integers with anagrams... @DEEM – El-Guest 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? – El-Guest May 13 '20 at 16:54
Regarding that second attempt, then the answer is no longer unique, no? – Sid May 13 '20 at 17:08
Yes, but the initial question never asked for a unique answer — up to DEEM, really! – El-Guest May 13 '20 at 17:14
Spelling is important. Forty is the MW dictionary spelling – DrD May 13 '20 at 17:50
3

Thank goodness, that would’ve been a copout of an answer – El-Guest May 13 '20 at 17:56

score 8 · Answer 5 · answered May 13 '20 at 19:20

8

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 !

answered May 13 '20 at 19:20

Tom

70,468
4
249
361

it took me a while, I was thinking that rot13(guerr uhaqerq naq svsgl friragu jnf guerr uhaqerq naq (svsgl friragu)) – melfnt 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

score 4 · Answer 6 · edited May 13 '20 at 19:31

4

46 and 64

Fourty Six and Sixty Four

64 - 46 = 18 > 5

edited May 13 '20 at 19:31

MacGyver88

5,261
2
12
43

answered May 13 '20 at 16:55

asanoop24

181
2

Think I ninjaed you if this is correct, but nice guess! – El-Guest 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. :) – asanoop24 May 13 '20 at 17:00
1

Spelling is important! Forty is the correct spelling – DrD May 13 '20 at 17:49
@DEEM..So this is not the correct answer?? – asanoop24 May 14 '20 at 06:53

score 2 · Answer 7 · answered May 13 '20 at 15:04

2

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 $\frac{60}5-\frac{50}6 = 3.66..$'

answered May 13 '20 at 15:04

daw

3,178
6
21

1

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

What number is that ? Asks Grandpa

7 Answers7

Linked