How to make four 7 s equal to 4 and to 10?

Question

How to make four 7 s equal to 4 and to 10?

f(7, 7, 7, 7) = 1: 7/7 * 7/7 = 1
f(7, 7, 7, 7) = 2: 7/7 + 7/7 = 2
f(7, 7, 7, 7) = 3: (7+7+7)/7 = 3
f(7, 7, 7, 7) = 4: ?
.
.
f(7, 7, 7, 7) = 10: ?
I can also make four 7s equal to 5, 6 , 7 , 8 and 9 by using square root and lg plus +, - * and / but not 4 and 10.

Unfortunately, puzzles tend to be swept away at this server (At least my experience with my puzzles). Hence, I decided to upvote it. — Peter, Feb 09 '17 at 21:50
You shouldn't need to use logs for $5,6,7,8,9$, but $\sqrt{7\times7}=7$ is useful. — Joffan, Feb 09 '17 at 21:57
$$7+(7-7)\cdot 7=7$$ $$7-\frac{7+7}{7}=5$$ $$7+\frac{7+7}{7}=9$$ — Peter, Feb 09 '17 at 22:15
So, upto $10$ , we only need "+,-,*,/". We can reach $12$ as well : $\frac{77+7}{7}=12$. What about $11$ ? $\frac{77}{7}$ would work, but how can we use $4$ sevens ? — Peter, Feb 09 '17 at 22:38

Peter · Answer 1 · 2017-02-09T21:45:58.317

4

$$\frac{77}{7}- 7=4$$

$$\frac{77-7}{7}=10$$

edited Feb 09 '17 at 21:45

answered Feb 09 '17 at 21:45

Peter

84,454

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Just $\frac{77}{7}-7$ is easier for 4 – Joffan Feb 09 '17 at 21:45
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@Joffan I my god, didn't get this! I become old! – Peter Feb 09 '17 at 21:46

score 0 · Answer 2 · answered Feb 09 '17 at 23:14

0

How about this: $|\{7,7,7,7\}|=4$. Seems obvious but don't know if it falls in line with acceptable mathematical operations!

answered Feb 09 '17 at 23:14

AloneAndConfused

1,739

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But ${7, 7, 7, 7}={7}$ . . . – Noah Schweber Feb 09 '17 at 23:46
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Here's a way to salvage the idea: $|{7}|+|{7}|+|{7}|+|{7}|=1+1+1+1=4$. – Théophile Feb 10 '17 at 00:32
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Quite right! The important lesson is to not answer posts late at night. Right idea but poorly executed - thanks for salvaging it @Theophile ! – AloneAndConfused Feb 10 '17 at 07:17

How to make four 7 s equal to 4 and to 10?

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