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Problem 302

Combinatorics Difficulty 1.6 Multiple choice CEMC Gauss (Grade 8) · Canada · 2025

Two standard six-sided dice are rolled. If the two numbers on the
top faces are multiplied, which of the following products is most
likely?

Pick one

Official solution

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.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.