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Algebra Difficulty 2.6 Junior Find the answer Canada

A numerical value is assigned to each letter of the alphabet. The
value of a word is determined by adding up the numerical values of each
of its letters. The value of SET is $2$ , the value of HAT is $7$ , the value of TASTE is $3$ , and the value of MAT is $4$ . What is the value of the word
MATH?

Pick one

Solution

There are $3$ different
colours and $4$ different numbers,
and therefore $3\times 4=12$
different kinds of robots that may be assembled. (These are R1, R2, R3,
R4, B1, B2, B3, B4, G1, G2, G3, G4, where R, B, G represent the $3$ colours red, blue, green.)

Since there are $12$ different kinds
of robots, it is possible that the first $12$ robots assembled are all different
from one another.

In this case, the $13$ th robot
assembled would be the first robot to have the same colour and the same
number as a previously assembled robot, and thus the greatest possible
value of $n$ is $13$ .

Notes:

It is possible that the first duplicate occurs earlier, but we
want the latest that it can occur.
There must be a duplicate robot among the first $13$ assembled, and so $n<14$ .
This solution makes use of the Pigeonhole principle – a
concept worth further investigation.

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