Product Value 60 Math Brainteaser

in StemSocial2 months ago

Hi there. In this math post, I go over this brainteaser that I was somewhat working on through my Mathnasium work. I spent about 10 minutes on this.

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This brainteaser can be found here. I have a screenshot below.

Each letter corresponds to a number where A = 1, B = 2, C = 3 all the way to Z = 26. The objective is to create valid English words in which the product of the letter values equals 60. In the screenshot, the word CAT works as it is `3 x 1 x 20 = 60`. The letter C is with 3, the letter A is with 1 and the letter T is associated with the value of 20.

To find other words, do consider the factors of 60. Think of numbers that are used for multiplication to obtain 60. Factors of 60 are `1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60`. Thirty and sixty would not be valid factors here are the number of English letters goes up to 26. I have included a table of number factors with their associated letters.

LetterNumber Value
A1
B2
C3
D4
E5
F6
J10
L12
O15
T20

The only vowels in this list are `A` and `O`.

Words I Got

Here are some of the words I got in this exercise.

• ale (1 x 12 x 5)
• lea (Lea is a name, 12 x 5 x 1)
• act (1 x 3 x 20)
• tac (20 x 1 x 3)
• bob (2 x 15 x 2)
• cade (3 x 1 x 4 x 5)

A full solutions .pdf for this brainteaser can be found here.

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A Good Exercise For Kids

This brainteaser exercise does have a bit of rules to follow at first. The CAT example is easy to follow. There is a bit of trial and error involved in obtaining valid words. This forces the participant to use creativity and problem solving skills to form words that meet the product value of 60.

Variations for this include a higher product value, doing addition instead of multiplication and limiting the number of letters in words (3 letter words vs 4 four letter words.)

Those who like Scrabble could give this exercise a try.

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