# “Twelve of a times” table

I found a math problem on Twitter.

However, as it was presented, its solution is trivial. I managed to make it a bit more challenging by muddling up some equations:

How do you solve the advanced version of the puzzle?

The flag is 1, because it's the multiplicative identity. The person must be 4, then, because 4 is the only number such that its square is <20 and >=10. The train must then be 6, as it's the second digit of 16. The car must be 9 and the X is 3, because 36 is the only other product of 4 and a single digit number that ends in 6. The present must be 2 and the boat 8, as 8 is the only single digit product of 4 that is not 4 or 0. The only digits remaining are 5 and 0, and conveniently, 5 * 4 = 20, giving us the theta as 5 and the check as 0.

• Correct. It is worth noting that one digit is attributed to a unknown symbol; this doesn't nullify the solution as the unknown symbol is unique. – dr01 Oct 10 '15 at 19:10

It is the

4

Times table, because

Look at the fourth line: flag times person equals person. Therefore flag equals 1. Now look at the third line. Person squared is a 2 digit number starting with 1 (flag). The only such perfect square is 16, so person=4 and underground train is 6.
Police car times 4 is 10X + 6, police car must be 4 or 9, but 4 is already assigned. Police car is 9, X is 3. Present times 4 equals boat, boat is a single digit multiple of 4, 4 is already assigned so boat equals 8 and present equals 2. Stop times 4 equals 20 plus tick, meaning stop must equal 5,6 or 7. 6 is already assigned, 5 makes tick equal zero, 7 makes tick equal 8 (already assigned) so stop is 5, tick is 0. 7 remains unassigned.

The man doesn't represent 0, so the flag must be 1. As the square of the digit represented by the man starts with 1 on the 3rd row, it's 16 (6 = bus sign) and the man is 4. On the first row, the box can only be 2 and the ship 8. The last row's product starts with 2 and ends with a digit that's not 4 or 8, so the OK sign is 0 and the theta one 5. As for the 2nd row, the product can only be 36, making the X sign 3 and the car 9.

From top to bottom:

4 times table:
$2 \times 4=8$
$9 \times 4=36$
$4 \times 4=16$
$1 \times 4=4$ and
$5 \times 4=20$