You can only use Addition, Subtraction, Multiplication, Division. This is for a math project for my daughter.
You can only use the numbers once and all numbers do not need to be used.
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4$\begingroup$ I don''t believe there is and answer to the question as stated. $\endgroup$– paparazzoCommented Nov 17, 2017 at 20:37
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7$\begingroup$ Is it possible a 4 got lost somewhere? $23=5*3+4*2*1$ $\endgroup$– kaineCommented Nov 17, 2017 at 21:50
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3$\begingroup$ Can you use concatenation? In other words, can you make a two digit number by putting two of the digits together? Like $1$ and $5$ could make the number $15$? $\endgroup$– Todd WilcoxCommented Nov 18, 2017 at 12:54
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4$\begingroup$ @SarahFritz Please tell us the average age of your daughter classroom (7 years old?, 17 years old?) and what was the teacher expecting for this math project? "impossible", "usage of concatenation", "usage of decimal point", "usage of exclamation point" (factorial), "usage of power notation", "usage of non-decimal base", etc.? Or was it just a typo from teacher? $\endgroup$– CœurCommented Nov 19, 2017 at 10:23
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16$\begingroup$ It's worth bearing in mind that setting a child a maths question that cannot be solved - without first introducing the concept of insoluble problems - may reinforce any feeling in the child that they are unable to answer maths questions and are therefore bad at maths. Such questions should be handled carefully to ensure that the discovery that there is no solution is a positive outcome for the child. $\endgroup$– Vince O'SullivanCommented Nov 19, 2017 at 11:03
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16 Answers
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As stated the problem is not possible. Here's an online solver to show that.
Lateral thinking options could fix it (like @Apep (reinterpretation of the list), @jlars62(decimal point (very clever)), or @hoffmale (factorials), or @sousben and @D Krueger (non-decimal)). Or allowing powers:
$5^2-3+1=23$
Or allowing concatenation.
answered Nov 17, 2017 at 20:13
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1$\begingroup$ Powers are not allowed: -1 No solution: +1 $\endgroup$ Commented Nov 17, 2017 at 22:41
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13$\begingroup$ @ElementsinSpace: powers were used as "lateral thinking" after explaining there is no solution. $\endgroup$– user10179Commented Nov 18, 2017 at 12:46
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1$\begingroup$ Per original question: You can only use each number once $\endgroup$ Commented Nov 19, 2017 at 14:50
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1$\begingroup$ This is what I arrived at independently. Using each number once. 5 squared uses 5 and 2. Squaring a number is multiplication. How semantic is the question? +1 - like the end of the calculation!! $\endgroup$– TimCommented Nov 20, 2017 at 9:25
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1$\begingroup$ You are, however, making an assumption (usually a good one) that the 23 stated in the title is base 10. puzzling.stackexchange.com/a/57085/37225 and puzzling.stackexchange.com/a/57082/37225 cleverly answer the question you "prove" is unanswerable. Every fact has assumptions underlying it. $\endgroup$– NH.Commented Nov 21, 2017 at 18:32
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One solution could be:
(5+3)*3-1
under the (possibly invalid) assumption that
the problem could be considered as using "1, two 3, and 5"
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15$\begingroup$ Wins the "lateral thinking" award... $\endgroup$– smciCommented Nov 18, 2017 at 1:34
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I guess we are not allowed to repeat the numbers:
35 - 12 = 23
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1$\begingroup$ This has to be the simplest possible answer. :) $\endgroup$– SidCommented Nov 17, 2017 at 18:59
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21$\begingroup$ concatenation is not allowed as per the OP, if it was , surely just concatenate the 2 and 3=> 23 $\endgroup$– Jason VCommented Nov 17, 2017 at 19:09
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4$\begingroup$ @JasonV, OP didn't say anything about that. And you can't concatenate the 2 and 3 because you must use all those four numbers. $\endgroup$– SeyedCommented Nov 17, 2017 at 19:12
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8$\begingroup$ when OP said "you can only use Addition, Subtraction, Multiplication, Division" they did not include concatenation. Therefore, this is out of scope. Also, OP did not say you must use all numbers nor only once. $\endgroup$– Jason VCommented Nov 17, 2017 at 19:14
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2$\begingroup$ @JasonV, I am sure you know that concatenating is not a part of mathematical operation. I think it is better wait and see what the OP thinks about these answers and we shouldn't talk on his behalf. $\endgroup$– SeyedCommented Nov 17, 2017 at 19:19
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$$ \frac{5}{.2} - 3 + 1 = 23 $$
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$\begingroup$ Please put answers in spoiler tags. $\endgroup$– anonCommented Nov 18, 2017 at 0:22
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3$\begingroup$ @DEEM : Just because $0.2 = 2/10$ does not mean "$.2$" entails division ... any more than $4 = 8/2$ means that "$4$" entails division. $\endgroup$ Commented Nov 19, 2017 at 23:49
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5$\begingroup$ Brilliant, but no. Had the question said "digits" this would work, but the question says "numbers" and the number .2 is not the same as the number 2. $\endgroup$ Commented Nov 20, 2017 at 6:07
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23, not using 1 or 5.
didn't even need to use any mathematical functions
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$\begingroup$ -1. You used an invalid operation (concatenation) that wasn't allowed in the post. $\endgroup$– NH.Commented Nov 21, 2017 at 18:20
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It's very straightforward:
(5*3+2)/1Or, as pointed out by Cœur, since all numbers need not be used:
5*3+2
Why this works:
Calculations are performed in base-7.
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$\begingroup$ You can remove the
/1as not all symbols are required. $\endgroup$– CœurCommented Nov 19, 2017 at 10:15
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This is the answer, only using 2 of the 4 proposed numbers:
5 * 3 = 23
How come, you say?
we used base 6 calculations
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Using concatenation:
25 - 3 + 1
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Using numbers more than once, but interesting sequence.
1*2+2*3+3*5 = 23
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$\begingroup$ Given that the question is unclear as to if we can use each number more than once, this answer is plausible... $\endgroup$– Jason VCommented Nov 17, 2017 at 20:55
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$\begingroup$ fibonacci new world order confirmed? $\endgroup$ Commented Nov 19, 2017 at 2:27
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Assuming concatenation is allowed then this is another answer:
13 + 2 * 5
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5
If factorial is allowed:
(5 - 1)! - 3 + 2 = 23
or
5 * (3! - 1) - 2 = 23
or
(2 + 1) * 3! + 5 = 23
or
5! / 3! + 2 + 1
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$\begingroup$ I think hoffmale means factorial, or at least that's what I would call the ! operator $\endgroup$– FoonCommented Nov 18, 2017 at 18:35
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$\begingroup$ @Mazura yeah, i meant factorial... bad/wrong translation from german $\endgroup$– hoffmaleCommented Nov 18, 2017 at 18:36
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5$\begingroup$ "factorial" is "Fakultät" in German, which is basically the same word used for an university "faculty" $\endgroup$– hoffmaleCommented Nov 18, 2017 at 18:43
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$\begingroup$ factorial was the first solution that came to my mind! +1 $\endgroup$ Commented Nov 20, 2017 at 6:56
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How about this
(3*2+1)*5 = 23 using HEX
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1$\begingroup$ HEX does not sound like addition, subtraction, multiplication or division. $\endgroup$ Commented Nov 21, 2017 at 8:29
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$\begingroup$ @boboquack Why can't I use hexadecimal, where the base is 16? $\endgroup$– SJFJCommented Nov 21, 2017 at 8:40
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$\begingroup$ Base conversion is a way around literally any of these puzzles, and gets quite boring if done over and over again (a couple of samples). It also doesn't answer the intended question, even if it does answer the literal question. Lastly, I argue that base 16 requires $(3\cdot2+1)\cdot5=23_{16}$, which requires an extra 16. $\endgroup$ Commented Nov 21, 2017 at 8:53
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$\begingroup$ @boboquack Ok, new to the site so I wasn't aware that it was considered boring. $\endgroup$– SJFJCommented Nov 21, 2017 at 9:09
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1$\begingroup$ @boboquack, boring or not, the question had better state that the number they want is $23_{10}$ if they are trying to rule out creative solutions. $\endgroup$– NH.Commented Nov 21, 2017 at 18:35
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Dr Xorile has determined that there is no solution to the problem as stated. So all that remains are out-of-the-box solutions. Some good approaches have already been presented, treating "+" as string concatenation, and changing bases among the best.
Here's what might be jokingly termed a statistician's approach:
You could attempt the question twice and take the average:
- 5(3+1)+2 = 22
- 5(3+2)-1 = 24
Average = $\frac{22+24}{2}$ = 23.
All conditions are fulfilled on each attempt. :D
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$\begingroup$ @NH. All crisp. Stochastic, maybe. :) $\endgroup$– LawrenceCommented Nov 21, 2017 at 22:44
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If we can use a number twice, then:
(2+2)*5+3 = 23.
OR: (2+2)*3*2*1-5+(2*2)
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2$\begingroup$ in that case, how about 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 = 23? $\endgroup$ Commented Nov 20, 2017 at 14:52
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$\begingroup$ @DanielVestøl My answer was before the OP edited the question $\endgroup$– SidCommented Nov 20, 2017 at 15:21
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(5^2)-3+1
Squaring a number is the same as multiplying it by itself, so this counts in my book.
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3$\begingroup$ I don't think that was the OP's intent. All other operations can be reduced to simple addition, and by breaking it down to this you are saying 5*5 which gives two 5s. If the OP says we can use the number twice, this works. $\endgroup$– Jason VCommented Nov 17, 2017 at 20:53
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2$\begingroup$ Basically the same as @DrXorile's answer. $\endgroup$ Commented Nov 17, 2017 at 21:12
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Perhaps,
Round of (51/2) - 3
That is
26 - 3 to fetch 23
Of course, this involves concatenation.
answered Nov 18, 2017 at 6:28