It literally reads that way!

Algebra Level 2

Given that t w o = 2 , s e v e n = 7 , e i g h t = 8 , t e n = 10 , t w e n t y = 20 , s e v e n t y = 70 , e i g h t y = 80 , \begin{array}{c}&two = 2, &seven= 7, &eight=8, \\ ten = 10, &twenty = 20, &seventy = 70, &eighty = 80, \end{array} find the value of o n e one .


Note: The left side of each equation above is a product of unknowns. For example, s e v e n = s × e × v × e × n = s × e 2 × v × n , seven = s\times e \times v \times e \times n=s\times e^2 \times v \times n, where 4 unknowns s , e , v , n s, e, v, n are used.


The answer is 100.

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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4 solutions

Sabhrant Sachan
Dec 28, 2016

e i g h t y e i g h t = y = 10 s e v e n t y s e v e n = t y = 10 , t = 1 t w e n t y t e n = t w y = 2 , w = 1 5 \dfrac{\cancel{eight}y}{\cancel{eight}} = y = 10 \\ \dfrac{\cancel{seven}ty}{\cancel{seven}} = ty = 10 , \hspace{5mm} t = 1 \\ \dfrac{tw\cancel{ent}y}{\cancel{ten}} = twy=2 , \hspace{5mm} w = \dfrac{1}{5}

t e n = 10 , e n = 10 , t w o = 2 , o = 10 o n e = 10 ⋅ 10 = 100 \begin{aligned} ten & =10, \hspace{5mm} en = 10, \\ two & =2, \hspace{8mm} o =10 \\ one & = 10\cdot10 =\boxed{100} \end{aligned}

33 Helpful 0 Interesting 0 Brilliant 0 Confused

That is one nice problem here! :D

Michael Huang - 4 years, 5 months ago

Wow! So very pretty!

Calvin Lin Staff - 4 years, 5 months ago

Very nice!

Irina Stanciu - 4 years, 5 months ago

the letters appear to have differing values dependent upon the word they are in , make it up as you go along

Wal Sheppard - 4 years, 4 months ago

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You raise a good point. This solution only establishes a necessary value for o n e one . The system of equations might not have a proper solution, hence the critique of "letters appear to have differing values".

For completeness, we need to ensure that there is (at least) a proper solution set. What is it?

Calvin Lin Staff - 4 years, 4 months ago
Mick Martucci
Feb 10, 2017

if eight = 8 and eighty = 80 then y = 10

if seven = 7 and seventy = 70 and y = 10 then t = 1

if t = 1 and y = 10 and twenty = 20 then wen = 2

wen = 2 and two = 2 and t = 1 so wen = wo and en = o

t = 1 so ten = en = o = 10

one = o X en = 10 X 10 = 100

3 Helpful 0 Interesting 0 Brilliant 0 Confused

This is the exact steps that I used to solve/create this problem. Well done!

Pi Han Goh - 4 years, 4 months ago
Elijah Odunsi
Feb 11, 2017

just follow the pattern of 2 7 8 1 2 7 8 1 just adding zeros on each round

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ritabrata Roy
Jul 14, 2018

O=10,n=10,e=1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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