Rudiments of tallying?

Logic Level 4

Submit the answer as the digits in each blank from 0 to 9 in order. As an explicit example, if you think the numbers in all blanks are 1, submit your answer as 1111111111.

Inspiration .

The answer is 2284322232.

2 solutions

Vishnu Bhagyanath
Jul 16, 2015

Start out by assigning any number to each box, in this case I shall start with $2$ since, unlike the problem listed as inspiration there will be 2 of each digit in the beginning.

You keep adjusting the values till it satisfies the entire box.

I don't know what better way there is to explain it so I'll tell you how I did it. Let me know if you didn't understand any step.

The following sequence indicates the count of each number from 0 to 9 in that order

$\text{2 2 2 2 2 2 2 2 2 2}$

$\text{2 2 12 2 2 2 2 2 2 2}$

$\text{2 3 12 2 2 2 2 2 2 2}$

$\text{ 2 4 11 2 2 2 2 2 2 2}$

$\text{ 2 4 11 2 3 2 2 2 2 2}$

$\text{ 2 4 9 3 5 2 2 2 2 2 }$

$\boxed{\text{2 2 8 3 2 2 2 2 3 2}}$

I don't even remotely get the solution, would you care to explain it , or the logic behind it ?

Ahmed Obaiedallah - 5 years, 10 months ago

Sure! So there is an initial state given by the problem, before you fill anything in: each number is listed twice (at the beginning of each line and in the middle). To describe this initial situation, we'd say that each number appears "2" times, hence "2222222222". But wait! We just added a bunch of 2s! "22(11)2222222". Now we have two extra ones! "2 4 (11) 2222222" now we have a four! "2 4 (11) 2 3 22222" now we have a three! "2 4 (11) 3 3 22222". But wait now we don't have as many twos! 2 4 (8) 3 3 22222! Now we have an 8! 2 4 8 3 3 22232! Wait, now we don't have any extra ones! 2 2 8 3 3 22232! And now we don't have extra fours! 228322232! Uhm. This actually works?! It works! We be done here.

Tan Ho - 5 years, 10 months ago

Now that's both very clear and helpful, putting the numbers in their places solves my problem which I never did trying to burn my brain out finding what's the problem with my solutions and also why one of them must be the sole solution

Thank you again for your time and explanation

Ahmed Obaiedallah - 5 years, 10 months ago

How are there 2 zeroes in the list??

Aparna Phadke - 2 years, 4 months ago

1732111211 fits

Aparna Phadke - 2 years, 4 months ago

Isn't the ans is 2284322232..??

Charlz Charlizard - 5 years, 7 months ago

Charlz Charlizard
Aug 16, 2015

Here the number of times of 0's and 1's will be just 2 as (0,1<2)..In ideal case there will be 2+10=12 number of 2's..If you change any value, there will be change in 3 values correspondingly and obviously number of 2's is not 2...So in total there will be minimum (in one sense) 4 places in which there will no 2's..Now 12-4=8..Now let's check placing 8 in 2's place..So 8's=3..But here 3's cannot be 3..So make 4's=3 and 3's=4..Solved ................................................................................................................................................. 0 1 2 3 4 5 6 7 8 9 ....................................................................................................................................... 2 2 8 4 3 2 2 2 3 2

Rudiments of tallying?

The answer is 2284322232.

2 solutions

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