Thrifty numbers Part 1

Logic Level 2

$\large{ \square \, + \, \square \, = \, \square \\ \square \, - \, \square \, = \, \square \\ \square \, \times \, \square \, = \, \square \\ \square \, \div \, \square \, = \, \square \\ }$

Given that the integers $1,2,\ldots,9$ are to be filled in all the twelve square boxes above such that all four equations above are satisfied.

What is the minimum possible distinct number of integers used?

Details and Assumptions

You can use the same integer more than once.
You are not required to use all nine integers.
Each square box can only fill in exactly one digit.

4 2 3 5

2 solutions

Cody Hubbard
Dec 15, 2015

Only the integers 1 and 2 need to be used 1 + 1 = 2, 2 - 1 = 1, 2 × 1 = 2, 1 ÷ 1 = 1,

Thank you. That's very similar to mine. The subtraction and division are actually red herrings, because we can get them from the addition and multiplication respectively.

In your solution, the corresponding division line would be $2 \div 1 = 2$ or $2 \div 2 = 1$ .

Chung Kevin - 5 years, 6 months ago

But you did not include 0 in this question? BTW, my imagination picked 2 & 4.

Saya Suka - 4 years, 6 months ago

Oh, that's a typo, sorry. Let me edit my comment.

2 & 4 is also a nice way!

Chung Kevin - 4 years, 6 months ago

Krishna Deb
Jun 11, 2017

I tried not overthink it. 1+1=2

2-1=1

2x1=2

2/2=1

Since only 1 & 2 have this property, it's 2 numbers. Other pairs will end up using 3 distinct numbers at best. Example -

4+4=8

8-4=4

4x2=8 or 8x1=8

8/2=4 or 8/1=8

How can ◻️◻️*◻️ equal ◻️?? How can a two digit number equal a one digit number??

Aca Car - 1 year, 5 months ago

Thrifty numbers Part 1

2 solutions

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