No love for 2 and 3
No love for 2 and 3
Form two numbers. The sum of them must be $100$.
For the first one you must use the digits $4$, $5$ and $6$ taken exactly once in this order. You cannot use other digits.
For the second one you must use the digits $7$, $8$ and $9$ taken exactly once in this order. You cannot use other digits.
The operations you may use for forming each of the numbers are $x + y$, $x - y$, $x times y$ and $x div y$. Division is math division, you cannot use computer integer division where 4/5 = 0. Operator precedence is respected. Each operation may be used multiple times
4/5 = 0
You cannot use other symbols (except $456789+-timesdiv)$
Example:
Sum is wrong $14+96=110 neq 100$, but everything else is ok.
8 Answers
8
$ 45_6 = 29 $
$ 78_9 = 71 $
$ 29 + 71 = 100 $
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Excellent! Probably the expected answer
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– xhienne
Sep 13 '18 at 8:32
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Yes, that's my solution. Congratulations!
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– bolov
Sep 13 '18 at 10:29
Implementing lateral thinking
The question does not specify which base, $B$, we are in. Only that we are using the digits $4$, $5$, $6$, $7$, $8$ and $9$ so this means that $B geq 10$. I will assume $B=12$ so that we additionally have the digits $a$ and $b$.
Then one answer is
$4 times 5 times 6 = a0$
$7+8+9 = 20$
$a0 + 20 = 100$
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not the solution I had in mind but it does respects all the requirements. As far as I am concerned it's correct and it's the best solution yet.
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– bolov
Sep 12 '18 at 13:01
That should work:
Number 1: $4 times (-5 + 6) = 4$
Number 2: $7 + 89 = 96 $
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Nice answer!! :D
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– El-Guest
Sep 12 '18 at 1:50
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Negation isn't in the list of allowed operations though.
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– Bass
Sep 12 '18 at 4:04
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From my understanding, negation and "(", ")" are not allowed. So this should be wrong.
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– npkllr
Sep 12 '18 at 8:51
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Good try. However, parenthesis aren't allowed because you can't use their symbols
( ). Also, negation even if it uses the allowed symbol $-$ isn't an operation you can use.$endgroup$
– bolov
Sep 12 '18 at 8:58
(
)
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Sorry all, I didn't read the question carefully enough.
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– xhienne
Sep 12 '18 at 9:08
With a bit of lateral thinking:
1st number: $ 4 times 5 - 6 = 14 $
2nd number: $ 7 - 8 - 9 = -10 $
$ 14 + (-10) = 4 $
Decimal to Binary: $ (4)_10 = (100)_2 $
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I like your answer. A step in the right direction. And your answer confirms that the lateral thinking tag is appropriate.
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– bolov
Sep 12 '18 at 9:05
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Wait, so this is not your expected answer?
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– npkllr
Sep 12 '18 at 9:08
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no, it's not the answer I had in mind
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– bolov
Sep 12 '18 at 9:08
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Hmmm, ok. How about a small hint: Do we need multiple numeral systems for your solution?
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– npkllr
Sep 12 '18 at 9:12
With some brute force I can confirm what we thought already: we do need some lateral thinking to solve this challenge!
In bash, try all combinations of operators (+, -, * and / and the concatenate character which is an empty string: ' '). No negation, no brackets.
Then print the ones where the outcome is between 95 and 105:
for a in + - * / ''; do
for b in + - * / ''; do
for c in + - * / ''; do
for d in + - * / ''; do
echo 4$a5$b6 + 7$c8$d9 = $(echo "scale=3 ; 4$a5$b6 + 7$c8$d9" | bc)
done
done
done
done | awk '$NF>95 && $NF<105,1'
Output:
4+5+6 + 78+9 = 102
4+5-6 + 7+89 = 99
4+5*6 + 7*8+9 = 99
4+5*6 + 78-9 = 103
4+5/6 + 7+89 = 100.833
4-5+6 + 7+89 = 101
4-5/6 + 7+89 = 99.167
4*5-6 + 78+9 = 101
4*5/6 + 7+89 = 99.333
4/5+6 + 7+89 = 102.800
4/5*6 + 7+89 = 100.800
4/5/6 + 7+89 = 96.133
4/56 + 7+89 = 96.071
45+6 + 7*8-9 = 98
45-6 + 7*8+9 = 104
45/6 + 7+89 = 103.500
So no luck here yet!
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Also, $(4times 5 + 6)+(78-9)=95$ is another close one :D
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– user477343
Sep 12 '18 at 11:48
Similar to npkllr's answer
$- 4 + 5 - 6 = - 5$
$78 - 9 = 69$
$-5 + 69 = 64$
$DEC(64) = OCT(100)$
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Negation isn’t allowed
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– DonielF
Sep 12 '18 at 13:56
I doubt this is what you're looking for, and is really stretching the limits of interpreting what you said, but:
1st number: 4×5−6
2nd number: 7+89
1st number: 4×5−6
2nd number: 7+89
Now, only using the allowed digits, the sum of 4 (1 is not an allowed symbol and therefore 14 becomes 4) and 96 is 100
4
96
4*5/6 = 3.33
7+89 = 96
3.33 + 96 ≈ 100
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Welcome to puzzling.SE! Unfortunately, the result must be exactly 100 (moreover 99.333 ≈ 99, not 100).
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– xhienne
Sep 12 '18 at 13:30
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@xhienne if ≈ stands for "approximately equal to", or "almost equal to" why is 99.333 ≈ 100 wrong? its still almost equal to the 99.333. ≈ does not mean round down. And even so, i could also go with 99 ≈ 100. Regardless of wether the sum is exactly 100.
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– Ano
Sep 13 '18 at 6:16
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the titles holds no clues. It's just fun (or lack of inspiration, take it as you will). It alludes to the fact that the digits $2$ and $3$ are the only ones not mentioned in the question.
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– bolov
Sep 12 '18 at 0:14