ROOTbeerr's Puzzling Riddle (With Prize)

Rootbeerr

The first one to solve this riddle will get 500c OR a fox tail.

Two mathematicians meet on a plane.
"If I remember correctly, you have three sons," says Ivan. "What are there ages today?"
"The product of their ages is 36," says Igor. "And the sum of their ages is exactly today's date,"
"I'm sorry, Igor," Ivan says after a minute, "But that doesn't tell me the ages of your boys,"
"Oh, I forgot to tell you, my youngest son has red hair," Replies Igor.
"Ah, now it's clear," Ivan says, "I now know exactly how old your three sons are,"
How did Ivan figure out the ages?

Good Luck! :D

PEgaming

Answer:

Step 1: Product
1x1x36
1x2x18
1x3x12
1x4x9
1x6x6
2x2x9
2x3x6
3x3x4

All these equal to 36.

Step 2: Dates

1+1+36 = 38
1+2+18 = 21
1+3+12 = 16
1+4+9 = 14
1*6*6 = 13
2*2*9 = 13
2*3*6 = 11
3*3*4 = 10

The greatest number of days in a month is 31, so it can not be 1,1,36. Well, there is a youngest son, so it couldn't work anyway.

1, 2, 18
1, 3, 12
1, 4, 9
1, 6, 6
2, 2, 9
2, 3, 6
3, 3, 4

Step 3: Youngest Son

This tells us that there is a youngest son, so bye bye 2, 2, 9 and 3, 3, 4.

Step 4: Tally em up.

Ages are 1, 2, 18, product of 36, sum of 21
Ages are 1, 3, 12, product of 36, sum of 16
Ages are 1, 4, 9, product of 36, sum of 14
Ages are 1, 6, 6, product of 36, sum of 13
Ages are 2, 3, 6, product of 36, sum of 11

So it could be these five.

500c pl0x

Stevenlol

PEgaming said:

Answer:

Step 1: Product
1x1x36
1x2x18
1x3x12
1x4x9
1x6x6
2x2x9
2x3x6
3x3x4

All these equal to 36.

Step 2: Dates

1+1+36 = 38
1+2+18 = 21
1+3+12 = 16
1+4+9 = 14
1*6*6 = 13
2*2*9 = 13
2*3*6 = 11
3*3*4 = 10

The greatest number of days in a month is 31, so it can not be 1,1,36. Well, there is a youngest son, so it couldn't work anyway.

1, 2, 18
1, 3, 12
1, 4, 9
1, 6, 6
2, 2, 9
2, 3, 6
3, 3, 4

Step 3: Youngest Son

This tells us that there is a youngest son, so bye bye 2, 2, 9 and 3, 3, 4.

Step 4: Tally em up.

Ages are 1, 2, 18, product of 36, sum of 21
Ages are 1, 3, 12, product of 36, sum of 16
Ages are 1, 4, 9, product of 36, sum of 14
Ages are 1, 6, 6, product of 36, sum of 13
Ages are 2, 3, 6, product of 36, sum of 11

So it could be these five.

500c pl0x

Same thinking as you, but i stopped at step 2 dates, since the only repeated day is 13, so the date is the 13th, that's the only way if Ivan could not tell the ages.

Now the question asks for the youngest: If it's 2,2,9: there is no youngest son
If it's 1,6,6: then that would be the only possible choice---

*Edited with spoilers*

A one year old is the youngest son, and 6 year old twins

500c if I got it right :D

PEgaming

Steven, the question asks for the ages of all three sons. As there is no more information given, it could be any 5 of those ages.

CD87

eagence said:

Easy, check my spoiler

Spoiler:

Step 0: Evaluation of Clues:

What we have?
- Product of ages of three son is 36 ( a x b x c =36)
- Sum of ages of three son is todays date ( a + b + c <31)
- There is a youngest son ( a<b and a<c)
- Question is exacty solvable when Igor edits in a way that Ivan knows age of all 3 sons

Hidden Clue due to "exacty solvablity" and not mentioning of an oldest son -> There is no oldest son so its solvable and Ivan may know whose age is exactly what ...

Step 1: Evaluation of Possible Product:

Assume ages are integers only. Factorize 36 into prime factors

1x1x36
1x2x18
1x3x12
1x4x9
1x6x6
2x2x9
2x3x6
3x3x4

All these equal to 36.

Step 2: Evaluation of Dates:

1+1+36 = 38 (canceled 38>31)
1+2+18 = 21
1+3+12 = 16
1+4+9 = 14
1*6*6 = 13
2*2*9 = 13
2*3*6 = 11
3*3*4 = 10

The greatest number of days in a month is 31, so it can not be 1,1,36. Canceled...


Step 3: Youngest Son:

1, 2, 18
1, 3, 12
1, 4, 9
1, 6, 6
2, 2, 9 (canceled no youngest but 2 sons at age 2)
2, 3, 6
3, 3, 4 (canceled no youngest but 2 sons at age 3)

Igor tells us that there is a youngest son, so 2, 2, 9 and 3, 3, 4 also canceled because

Step 4: Rightness/Solvability & Exactness of question/riddle

This part is tricky, in order to ask it properly Igor says "Oh, I forgot to tell you, my youngest son has red hair," and makes it solvable and the only case that is solvable is:

Ages are 1, 6, 6, product of 36, sum of 13

because in all other case first there is no oldest son which is not mentioned, (so its generally assumed not), second question is not solvable if there is an oldest son existing so there isn't since we assume Igor asked question right, after saying "Oh, I forgot to tell you, my youngest son has red hair,". In case there is an oldest son Ivan can't know which of that 4 choices. Third even there is an oldest son Ivan can't know exactly because one boy will be older than other so which one will it be? who is who? and how he will eliminate these 4 cases and select the right one?

So due to the rightness solvability and exactness of question based on Igor's expression, there has to be no oldest son so:

1, 2, 18 (canceled because there is an oldest son)
1, 3, 12 (canceled because there is an oldest son)
1, 4, 9 (canceled because there is an oldest son)
1, 6, 6 (RİGHT ONE)
2, 3, 6 (canceled because there is an oldest son)

it becomes not solvable in any other case its the clue given, and they are mathematicians they ask right in riddles, thats the logic XD

Its a bit complex to tell I hope its clear....

I am absolutely agree with this answer xD

Stevenlol

Isn't that what i said? o.o