Messy Kid

Logic Level 1

A messy kid wrote a multiplication problem.

  • Alice saw: 100 × 6 100 \times 6
  • Josh saw: 101 × 6 101 \times 6
  • Dan saw: 102 × 9 102 \times 9

Each one only misread one digit. What is the answer to the real problem?


The answer is 612.

Leafy Li by Leafy Li , 30, USA

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5 solutions

Leafy Li
Feb 28, 2019

If the multiplication problem had been ??? X 9, then either Alice or Josh misread 2 digits. So we know it must be ??? X 6. Dan's 102 must be correct, or else he messed up 2 digits. Therefore, the answer is 102 X 6, or 612 \boxed{612}

21 Helpful 11 Interesting 15 Brilliant 3 Confused

Interesting, 100 6 = 600, 101 6=606, but 102*6 =612, in 3 case there 2 digit is need to change

player Dnf - 2 years, 2 months ago

Looks like people are confusing between number and digit and also not realising that the kids only saw the 'problem' and there were no solutions at the time. Actually this problem has two parts. First to find out what was the actual problem written on the board which the kids misread. Let's start with Dan. Had 1 been misread (9 written correctly) then both Alice and Josh had misread two figures each (9 and 1) which is not correct. Same argument goes for 0. Had 2 been the misread digit then this digit could have been 0, 1, or any other digit. In the last scenario again both Alice and Josh would have misread two digits. In either of the first two cases only one of Alice or Josh would have misread exactly one digit while the other would have misread two. So that also is correct. This leaves 9 as wrong. Now if 102 is correct then Alice and Josh both read 2 incorrectly thus they read 6 correctly so the correct problem was 102 x 6 and on double checking it shows that all of them misread only one figure out of four (0 by the first two and 9 by Dan). The solution to this problem is obviously 612

Zahid Hussain - 1 year, 11 months ago

Alice & Josh saw that either 100 or 101 was the first number, but both think that the last number is 6. This says that 6 is the last number. We replace the 9 with 6 in what Dan saw, so that means the real problem is 102 X 6. The answer is 612.

2 Helpful 0 Interesting 1 Brilliant 0 Confused

Just a question: how do you know which of the three wrote the 1st number correct?

Digital Gaming 227 - 10 months, 3 weeks ago

Because Alice and Josh saw x6 and their initial number (100/101) varied, x6 has to be correct. Dan saw x9 incorrectly, meaning he saw 102 correctly so the answer is 102 x 9 = 612.

0 Helpful 0 Interesting 1 Brilliant 0 Confused
Linda Mudland
May 28, 2020

If they all read 1 digit wrong then it is something times 6. 102 times 9 means it has to be 102 times 6 because otherwise they'd see 2 digits wrong.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Justin S.
May 7, 2019

Alice saw two numbers: 100 and 6

Josh saw two numbers: 101 and 6

Dan saw two numbers: 102 and 9

Each student only missed 1 number, meaning the other number was correct.

If Alice and Josh both had the same numbers as one of their factors but different numbers for their second factors we can deduce that they each correctly wrote the repeated factor.

They can only make one mistake so the repeated number has to be the correct factor. If they both wrote the same digits we wouldn't have been able to deduce which numbers were correctly seen and which were read incorrectly. The different factor proves the correct factor.

Now we know that 6 is the correct factor we know that Dan misread the 6 as a 9 . Therefore 102 is the other correct factor.

Only problem I have with this question is that Dan could have misread the 6 as a 102...somehow... and we could just as easily prove that 9 was the correct factor

With variables

A: m*n

J: p*n

Therefore n is factor

D: x*y

How do we know which one he misread?

0 Helpful 0 Interesting 0 Brilliant 3 Confused

Oh that is simple! He would have misread three digits if he mistaked 102 as 6, because it would be misreading 102 as 006, misreading the 0, 0, and 6.

Leafy Li - 1 year, 10 months ago

1 pending report

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