Problem 222

In the grid shown, the first column and first row
show the possible numbers that may appear on the top faces of the two
dice.

The inside of the grid shows the product of the corresponding two
numbers.

$\times$
$1$
$2$
$3$
$4$
$5$
$6$

$1$
$1$
$2$
$3$
$4$
$5$
$6$

$2$
$2$
$4$
$6$
$8$
$10$
$12$

$3$
$3$
$6$
$9$
$12$
$15$
$18$

$4$
$4$
$8$
$12$
$16$
$20$
$24$

$5$
$5$
$10$
$15$
$20$
$25$
$30$

$6$
$6$
$12$
$18$
$24$
$30$
$36$

Of the results, a product of $4$
appears $3$ times, a product of $6$ appears $4$ times, a product of $9$ appears $1$ time, a product of $15$ appears $2$ times, and a product of $8$ appears $2$ times. Thus, of the possible products
given, $6$ is the most likely to
occur.