Multiplication Table

Probability Level 3

Lila is on the process of memorizing the multiplication table. Now, she has memorized the table from rows 1-10 except rows 5, 7, and 8. Assuming that she has fully memorized all other rows, and she knows how the commutative property of multiplication works, then how many combinations left does she have to take note to fully memorize the $10 \times10$ multiplication table?

Clarification:

$1 \times 2$ and $2 \times 1$ comprise one combination.

The answer is 6.

2 solutions

Efren Medallo
May 6, 2015

If Lila has learned all other rows except rows 5,7, and 8, then she will not have a problem memorizing yhe other numbers in these rows that involve one number from other rows (e.g. 5x3, 5x4, 7x3, etc). All that's left for her to memorize are those combinations involving numbers from those unknown rows. These are: 5x7, 5x8, 7x8, 5x5, 7x7, and 8x8. Since Lila knows the commutative property, she will automatically know 7x5, 8x5, and 8x7.

Jihoon Kang
May 4, 2015

If Lila has learned all the table except row 5, 7 and 8, this means she has learned the columns of 5, 7 and 8. Using the property of commutativity of multiplication, she knows the rows 5, 7 and 8 except for the squares $5×5$ , $7×7$ and $8×8$ . There are $3!=6$ ways of learning these three numbers.

Actually, she don't know $5×7$ , $7×8$ , or any intersection between the 3 columns and the three rows.

khaled Adel - 6 years, 1 month ago

Then your answer should have been 3, right? But the answer is 6.

Efren Medallo - 6 years, 1 month ago

Multiplication Table

The answer is 6.

2 solutions

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