Number 88 from the digits 2, 0, 1 and 7?

Question

Can you use the digits 2, 0, 1 and 7 each only once to create the number 88?

What are the allowed operations? Just +, -, / and * or can we use powers, factorials, etc? — hexomino, Feb 03 '17 at 14:19
@darkdemise if all you want it to get close, just do 7X12 or 170 / 2. no need to work so hard XD — stack reader, Feb 03 '17 at 14:36
@Pharap Exactly what I was thinking. 201*7+88 uses each of the digits 2, 0, 1 and 7 only once. I'm guessing no. :) — hvd, Feb 04 '17 at 12:01
I've brute-forced this problem with addition, subtraction, multiplication, division, exponentiation, negation, and factorial and not found any result for 88 (or a bunch of other positive integers below 100, for that matter). On to square roots and modulo operations... — ETHproductions, Feb 04 '17 at 23:45
the number 88 is nazi symbology, given that H is the eighth letter of the alphabet, and a person with the initials HH being very important to neo-nazis.... I would dare to say OP is absolutely trolling this SE. — Rosa, Feb 06 '17 at 02:31

score 60 · Accepted Answer · answered Feb 03 '17 at 14:44

60

What about this

$\left(\frac{0!}{.\overline1}\right)^2 + 7 = 88$

where

$.\overline1 = 0.1111\ldots$

answered Feb 03 '17 at 14:44

hexomino

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This is very nice! – Jeff Zeitlin Feb 03 '17 at 14:58
5

Why is this accepted? – minseong Feb 04 '17 at 18:00
2

@the why shouldn't it be? – Nick T Feb 05 '17 at 22:43
1

@Nick well, the OP never actually told us what they were after. I'm just wondering why the OP considered this a better answer than all the others. – minseong Feb 05 '17 at 22:48
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@theonlygusti, then ask OP and not the answerer. :P $\quad$ – Feb 06 '17 at 13:52
@theonlygusti My guess is because it appears to be the first answer and it meets the challenge. – Engineer Toast Feb 07 '17 at 13:11
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This one also seems to add the least amount of handwavium to get to the solution. – tfitzger Feb 08 '17 at 21:39
@tfitzger, Handwavium... I like that element! – NH. Nov 21 '17 at 18:39

score 53 · Answer 2 · answered Feb 04 '17 at 20:49

53

No rules?

Looks like 88 to me if I squint.

answered Feb 04 '17 at 20:49

Andrew Morton

667
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Looks right to me – Raystafarian Feb 07 '17 at 19:41

score 33 · Answer 3 · answered Feb 03 '17 at 20:32

33

Because modern math is done with computers, here's some Python:

>>> int(str(0 + 1 + 7) * 2)
88

answered Feb 03 '17 at 20:32

Alex H.

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I disagree that modern maths is done with computers. See the IMO and other related mathematics competitions. – boboquack Feb 03 '17 at 23:52
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Similarly in C#: new string((1 + 7).ToString()[0], 2) – Jeppe Stig Nielsen Feb 04 '17 at 11:15
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@boboquack Long-distance running is one of the best known competitions in the Olympics; still, modern commuters drive. – Nat Feb 04 '17 at 16:19
If you're going to do something like this, why not use BF? You just put 2017 in the front, and then put the BF code after. – Qwerp-Derp Feb 05 '17 at 04:27
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I'm not sure is string manipulation is a mathematical operation – user902383 Feb 06 '17 at 10:17
@user902383 point out where in the op mathematical operations are mentioned, let alone required – minseong Feb 06 '17 at 17:41
Tag [tag:mathematics] was added afterwards by another poster – smci Feb 07 '17 at 10:39

score 26 · Answer 4 · edited Feb 05 '17 at 18:18

26

For that matter:

In base 86: $12 + 0*7$

edited Feb 05 '17 at 18:18

Melkor

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answered Feb 03 '17 at 16:59

Bob DeMattia

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This does answer the question. In base 86 the numerals 12 = 88 in base 10. Adding the 0*7 in just a cheeky way of disposing of two useless numbers. How do I create 88 from 1, 2, 0 and 7? Change the base! – EvSunWoodard Feb 03 '17 at 20:20
4

In base 86, the number OP asked for doesn't exist. So no, it doesn't answer the question. – Josh Part Feb 03 '17 at 21:23
11

@Josh Sure it does. 88 base 10 = 12 base 86, which Bob used. Or, the other way around 88 base 86 = 696 base 10. – Graipher Feb 03 '17 at 22:46
Here is a good example of where the question asked needs to have proper constraints. I see another answer which involved changing the base. And to take the unconstrained problem one step further, someone even suggested that superimposing 1 over 2, and 7 over zero looks like 88. In my own defense, no one would argue that 0xf is 15. I don't see how saying "12 base 86 is 88" is any different. – Bob DeMattia Feb 06 '17 at 02:34
@BobDeMattia Really? Because the only information I can find on 0xf is that it's the number 15. – JMac Feb 06 '17 at 13:06
This answer uses 8 and 6... – M.Herzkamp Feb 06 '17 at 16:00
@JMac That's what I said! – Bob DeMattia Feb 06 '17 at 19:37

score 21 · Answer 5 · edited Feb 03 '17 at 15:24

21

If floor were allowed, then this works:

$\left\lfloor\sqrt{10!!}\right\rfloor + 27 $

because

$10!!$ is $10\cdot 8\cdot 6\cdot 4\cdot 2 = 3840 $
$\sqrt{3840} = 61.9677335393\cdots.$

edited Feb 03 '17 at 15:24

Ankoganit

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answered Feb 03 '17 at 15:19

Matt

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Rubio · Answer 6 · 2017-02-05T15:57:30.030

12

The only digits used here are 2,0,1,7 to reach 88:

$(\textbf{10}+(i\times i))^\bf2\rm+\bf7 = 88$

edited Feb 05 '17 at 15:57

answered Feb 05 '17 at 06:56

Rubio

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4

With this you could literally make any number though. Start at some number and add any amount of i^4 as required. – orlp Feb 05 '17 at 19:13

Jonathan Allan · Answer 7 · 2017-02-03T17:35:14.737

11

We can do it without the $0$...

$S=\{1,2,7\}$

$(\sum{S}-|S|)\times\prod{S}-\sum{S}$

(using the sum, $\sum$, cardinality, $||$, and product,$\prod$, of the set $S$.)

Evaluated:
$=(10-3)\times 14-10$
$=7\times 14-10$
$=98-10$
$=88$

So, obviously we could just add zero afterwards.

Mind you, I suppose that we could also do it with just one of the numbers in that case too.

$S = \{x\}$

$(|S|+|S|+|S|+|S|+|S|+|S|+|S|+|S|+|S|+|S|+|S|)\times(|S|+|S|)\times(|S|+|S|)\times(|S|+|S|)$
$=(1+1+1+1+1+1+1+1+1+1+1)\times(1+1)\times(1+1)\times(1+1)$
$=11\times2 \times2 \times2$
$=88$

...so
For $x = $...$7$, $2$, or $1$ just multiply the rest together and add them on.
For $x=0$ one can add $(7\times 2)\pmod{1}=0$, or $(7+1)\pmod{2}=0$.

The only question is: Does doing what I have done here count as using the given numbers more than once?

Here is an alternative, sneaky way...

Subtract the one from the seven, turn the resulting six upside-down, append the zero, then subtract the two.

$7-1=6$
$\text{turn}(6)=9$
$\text{append}(9,0)=90$
$90-2=88$

edited Feb 03 '17 at 17:35

answered Feb 03 '17 at 16:32

Jonathan Allan

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Just add a $+0$ onto the end. – Deusovi Feb 03 '17 at 16:36
4

I'm a big fan of the sneaky way. – EvSunWoodard Feb 03 '17 at 20:20
2

Why not x = 2 * 0 * 7 + 1, and then x + x + x + ... + x = 88? Seems like once you're allowed to define variables, the challenge is lost. – Dietrich Epp Feb 04 '17 at 08:26
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if you are allowed to use sets you don't need any digits. – Jasen Feb 04 '17 at 09:01
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define sneakyfunc(2,0,1,7) = 88. – Neil W Feb 04 '17 at 09:20
@DietrichEpp Agreed - it's borderline - hence why I wrote "Does doing what I have done here count as using the given numbers more than once?" (the question does say "digits". The reason I gave the first answer is that using a set is not exactly the same as using a variable as I am using its properties rather than as a placeholder to actually reuse the digits themselves. – Jonathan Allan Feb 04 '17 at 11:44
@NeilW wow, now that is sneaky. – Jonathan Allan Feb 04 '17 at 11:45
@Jasen, Yes I suppose so! (you mean like $A={}$, $B={A}$, $|B|=1$?) – Jonathan Allan Feb 04 '17 at 11:46
yeah, |{{}}|=1 so 88= (|{{}}|+|{{}}|+|{{}}|+|{{}}|+|{{}}|+|{{}}|+|{{}}|+|{{}}|)(|{{}}|+|{{}}|+|{{}}|+|{{}}|+|{{}}|+|{{}}|+|{{}}|+|{{}}|+|{{}}|+|{{}}|+|{{}}|) – Jasen Feb 06 '17 at 12:03

score 7 · Answer 8 · answered Feb 03 '17 at 16:19

7

If ceiling or nearest integer function is allowed,

$\lceil{\tan^{-1}(27+0!)}\rceil = 88^{\circ}$

answered Feb 03 '17 at 16:19

Timtech

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That's the cleverest use of the 1, I think... to turn tan into arctan. – NH. Nov 21 '17 at 18:42

score 5 · Answer 9 · answered Feb 06 '17 at 13:31

5

Use "2" and "0" as digital numbers to combine them to form "8"
Add "1" and "7" mathematically and the result is "8"

So "88"

answered Feb 06 '17 at 13:31

rizzz86

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gogators · Answer 10 · 2017-02-03T21:45:46.533

4

As a perl one-liner you could write:

perl -le 'for ($_=-1-2,$i = 0; $i<7; $i++) {$_+= $i*$i }; print'

or without a zero:

perl -le 'print ((7+1)x2)'

or without a zero OR a two in the bash shell:

x=$((7+1)) && echo $x$x

or without a zero, one, or two in bash:

false || x=$((7+$?)) && echo $x$x

or without any numbers at all:

false || x=$(($?+$?+$?+$?+$?+$?+$?+$?)) && echo $x$x

edited Feb 03 '17 at 21:45

answered Feb 03 '17 at 21:39

gogators

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The puzzle is tagged [mathematics], not [programming]. – Glorfindel Feb 03 '17 at 21:43
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@Glorfindel the puzzle is also tagged [calculation-puzzle]. my answer involves both mathematics and calculations. – gogators Feb 03 '17 at 21:49
1

You could build any number you want. this way. No fair! :D – CoffeDeveloper Feb 04 '17 at 04:08
1

...or in English eighty-eight. – Jonathan Allan Feb 04 '17 at 11:32

score 2 · Answer 11 · answered Feb 03 '17 at 16:53

2

If we use base 36

We now have access to the digits 2, 0, 1, A, N, D, 7. So:
$= (N \times D) - 7 + \left(\frac{A}{2}\right) - 1 + 0$
$= 8B - 7 + 5 - 1 + 0$
$= 8B - 3$
$= 88$
Using base 10 math gives us 2, 0, 1, 10, 13, 23, 7
$= (23 \times 13) - 7 + \left(\frac{10}{2}\right) - 1 + 0$
$= 299 - 7 + 5 - 1 + 0$
$= 299 - 3$
$= 296$
296 is 88 in base 36

answered Feb 03 '17 at 16:53

coffeecop

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2

But that's not what the question is asking for. – Rand al'Thor Feb 03 '17 at 17:19
1

The question says using those four digits once only. Your answer is the equivalent of saying "well, if I also use these other digits, I can get the answer!" which is completely besides the point. – Nij Feb 03 '17 at 22:49
Using the digits "2 0 1 and 7", if extract_digits=lambda x:set(" ".join(x).split()). However, the usual definition is extract_digits=lambda x:set(parse_english(x)). – wizzwizz4 Feb 04 '17 at 15:26
Why are we allowed to use $D$? I can agree with using $A$ in base 36 as a creative way of using $1$ and $0$, especially since the question never specified base 10, but why is $D_{36} = 13_{10}$ ok? – Feb 06 '17 at 13:59

score 2 · Answer 12 · answered Feb 04 '17 at 05:34

2

Here is my first answer after about 5 minutes of brute-force checks!

$\lceil\log{\sqrt{102!}}\rceil+7=88$

where log means logarithm in base 10.

By the way, as a wild guess, I think that 88 is very likely to be the OP's birth year.

answered Feb 04 '17 at 05:34

Or, perhaps, age. You can never tell, unless you're a data miner or have access to said data miner's data. – wizzwizz4 Feb 04 '17 at 15:29
@wizzwizz4 This could have been another puzzle. And we can never be sure about a puzzle's solution until the puzzle owner reveals the answer... – Feb 04 '17 at 15:33
1

It's the visual representation of a 7-bar numerical display. Interpreting it as such gives 1111111 1111111. ASCII has seven bits; interpreting this number as ASCII gives DEL DEL. The OP wants to delete all puzzles. – wizzwizz4 Feb 04 '17 at 15:41
@wizzwizz4 Add some evil laughs to the background – Feb 04 '17 at 17:28
I thought $88$ was a reference. – Feb 06 '17 at 14:01

score 1 · Answer 13 · edited Feb 07 '17 at 02:14

1

$0!-(.7-.1)\times.2$

$= 1 - (0.6)(0.2)$

$= 1 - 0.12 = 0.88$

remove the decimal point to get $088=88$.

edited Feb 07 '17 at 02:14

Jonathan Allan

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answered Feb 06 '17 at 10:05

JMP

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score 1 · Answer 14 · answered Feb 06 '17 at 12:07

1

In base 9:
$$88 = 102 - \lceil\sqrt 7\rceil$$

answered Feb 06 '17 at 12:07

Ry-

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score 1 · Answer 15 · answered Feb 06 '17 at 19:38

Here is yet another one.

$$\lceil{\sqrt{\sqrt{\left(\sqrt{\sqrt{7!}}\right)!} \times \left( 2 + 0! + 1\right)!}\rceil}$$

Breaking it down:

$$7! = 5040$$ $$\sqrt{7!} = \sqrt{5040} = 70.992957$$ $$\sqrt{\sqrt{7!}} = \sqrt{70.992957} = 8.42573$$ $$\left(\sqrt{\sqrt{7!}}\right)! = 8.42573! = 101358.44566$$ $$\sqrt{\left(\sqrt{\sqrt{7!}}\right)!} = \sqrt{101358.44566} = 318.368411$$ $$ \sqrt{\left(\sqrt{\sqrt{7!}}\right)!} \times \left(2 + 0! + 1\right)! = 318.368411 \times 24 = 7640.84$$ $$\sqrt{\sqrt{\left(\sqrt{\sqrt{7!}}\right)!} \times \left(2 + 0! + 1\right)!} = \sqrt{7640.84} = 87.412$$

$$\lceil{\sqrt{\sqrt{\left(\sqrt{\sqrt{7!}}\right)!} \times \left( 2 + 0! + 1\right)!}\rceil} = \lceil{ 87.412 \rceil} = 88$$

score 1 · Answer 16 · answered Feb 07 '17 at 02:10

1

Another use of mathematical functions and flooring...

$\lfloor\ln\Gamma(\frac{7\times10}{2})\rfloor$

$=\lfloor\ln\Gamma(35)\rfloor$

$=\lfloor88.58082754219768\rfloor$

$=88$

Reference: $\ln\Gamma(x)$

answered Feb 07 '17 at 02:10

Jonathan Allan

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score 0 · Answer 17 · answered Jun 26 '19 at 19:51

0

If subfactorial is allowed:

$!(7-2)\times(1+0!)=44\times2=88$

answered Jun 26 '19 at 19:51

ThomasL

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Number 88 from the digits 2, 0, 1 and 7?

17 Answers17

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