PLEASE HELP!!

Hello everybody!! I had my FTRE(FIITJEE TALENT REWARD EXAM) yesterday.This exam is held all over India and I think you all must have understood the purpose!There was this question that I have no idea how to solve and I was thinking if someone could help me.Anyway,the question is,ab‾×c‾=def‾\overline{ab}\times \overline{c}=\overline{def}.These conditions apply on the digits,(a,b,c,d,e,f):∙they are distinct∙none of them is equal to 0∙they are all less than 7.(a,b,c,d,e,f):\\ \bullet they\ are\ distinct\\ \bullet none\ of\ them\ is\ equal\ to\ 0\\ \bullet they\ are\ all\ less\ than\ 7.Find the digits.

#Algebra #NumberTheory #Ilovenumbertheory

Note by Adarsh Kumar
6 years, 5 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list
  • bulleted
  • list

1. numbered
2. list
  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai−1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 ∑i=13 \sum_{i=1}^3
\sin \theta sin⁡θ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

54×3=16254\times 3=162

Aneesh Kundu - 6 years, 5 months ago

Log in to reply

awesome!Could you please tell how you got that.

Adarsh Kumar - 6 years, 5 months ago

Log in to reply

  • Firstly since all the digits are distinct so b,c,f≠5b, c, f\not = 5, moreover dmax=3d_{max}=3 ( max occurs at 54×6=32454\times 6=324 )so only a=5a=5 or e=5e=5 .

  • b,c≠1b,c\not = 1(as that would result in repetition)

  • f≠1f\not = 1 (as 1 would occur only at u(1×1)=1u(1\times 1)=1, u(7×3)=1u(7\times 3) =1, u(9×9)=1u(9\times 9)=1 none of which satisfy the conditions.)

We start with a=5a=5,

  • If b=2b=2 , then cc can be 3,63, 6

  • If b=3b=3 , then cc can be 2,42, 4

  • If b=4b=4 , then cc can be 33

  • If b=6b=6 , then cc can be 22

A quick check gives us the solution.

NOTE

  • In the last step we cross out some values which give us a bigger unit's digit than 6 or if a repetition occurs.

  • u(x)u(x) means unit's digit of xx.

Aneesh Kundu - 6 years, 5 months ago

Log in to reply

@Aneesh Kundu – Thanx dude!

Adarsh Kumar - 6 years, 5 months ago

54 *3 = 162

Palash Som - 6 years, 5 months ago

Log in to reply

yup!that is correct!

Adarsh Kumar - 6 years, 5 months ago

See such questions could by setting few conditions by ourselves-

lets take it that way -- if b =x then c must be what such that f is not equal to c or b

If we put b as 1 then all values of f would be equal to c.

If we put b as 2 we see that c could be = 3

If we put b as 3 we see that c could be = 2 , 4

If we put b as 4 wee see that c could be = 3

5 can never stand on our suppositions

even 6 won't be

so we examine the 4 values of b = 2, 3 , 4 and c also 2 , 3 , 4

then we think for value of a

If a = 1 then it won't be 3 digit number . Similarly even 2 won' t be - Then further we could do trial & error wid the remaining values

hence , 54*3 = 162

Palash Som - 6 years, 5 months ago

54x3=162

Manit Kapoor - 6 years, 5 months ago

Log in to reply

thanku!

Adarsh Kumar - 6 years, 5 months ago
×

Problem Loading...

Note Loading...

Set Loading...