The famous 90 x 3 + 20 puzzle.

I first heard a variant of this puzzle back in school, that’s going back to the early 1980s. Lets see how many can solve it.

This is not as simple as you may think. It is good to let an ageing brain do some work.

Three men went to a hotel to share a room.

The clerk asked for $300.

Each man paid $100, making up the $300.

The hotelkeeper then decided to allow a discount for the day, charging only $250 for the room.

He told the clerk to return $50 to the three men.

The clerk pocketed $20 for himself. He gave the remaining $30 back to the three men.

Each man took back $10. Therefore, each man paid 100 – 10 = $90 to the hotel.

$90 x 3 = $270 + the clerk’s $20 = $290.

Question: Where has the remaining $10 gone?

34 thoughts on “The famous 90 x 3 + 20 puzzle.”

  1. 10$ is gone no where, its sometime u do calculation backwards n create such results like counting backward fingers from 10 to 6 in one hand and then adding 5 into 6 of other wont make me having a hand with 11 fingers.
    actually they paid 250 altogether as u said and as the clerk decided the discount then adding the amount of the tip 250 + 20 makes 270 and atlast the 30$ all three men getting in return makes 270 + 30 = 300$
    wolla! puzzle solved :D

  2. You’re double counting there.
    Room’s for 250 and the clerk charged 20.
    Each person got 30 back; this accommodates the 300.
    If you consider the 90 route you include the clerk’s charge and re-add to cause the missing 10 conundrum.

  3. Clerk’s $20 are already included in the $270. You are counting them twice. What clerk kept for himself, also came from men’s pockets, not from somewhere else.
    So, out of 270 paid by the men, 250 went to hotel account and 20 went to the Clerk’s pocket. Simple as that.

  4. Now the total paid is $270 and not $300. :-)

    Total Paid by three men $90 * 3 = 270
    Clerk kept $20
    Housekeeper got $270 – $20 = $250

    In other words out of total $300
    Three men now have $30
    Clerk has $20
    Housekeeper has $250
    ($30+$20+$250=$300)

  5. Clerk’s 20 shouldn’t be added to the 270.

    Since the men actually paid 270, where as the rent was 250, remaining 20 were pocketed by the clerk.

  6. This is all about when you actually realized your expense and discount. :)
    If you consider this from simple arithmetic perspective then you would have problem to solve it.

    Actual spending is $250 so everyone paid $83.333 and they received $10 it becomes 93.333 for each.
    So we should think like this:
    93.333 * 3 + 20 = 300

    Math is fun!

  7. In $90 each you have added clerk rupees also now you have to add $30 they got discount this will become $300.

  8. You can not add the clerk’s amount with $270 to get the net figure $300 because the three man paid $270(i.e each man $90) has already included the clerk’s amount in it and the remaining are those $30 which has been returned by the clerk.

  9. The 270$ already contains the 20$ so you shouldn’t add it again instead the correct way to sum all the figures would be 250$ (with the hotel keeper) + 20$(with the clerk) + 10$ + 10$ + 10$ (10$ returned to each of the guests) = 300$. Solved

  10. instead of adding poketed 20 in 270 which make it controversy..
    so minus 20 then add 30 make 300 as follows…
    they paid 270 included 20 poketed took back 30 make 300
    250+30+20=300….mathmatic solved….easy way…nice solution

  11. my dear the 90+90+90=270$ which were given by those three men includes the $20 which has been taken by the waiter,therefore overall $270 were spend including bill of $250 and waiter’s$20.there us no question of $300

  12. It is double counting . Like if we count the fingers and thumbs , first hand from 1 to 5 and second hand from 10 to 6 than total fingers become 11 but we have got 10 ( 8 fingers 2 thumbs.)

  13. Multiplication does not work like that [(5+10) x 2] =/= [(10 x 2) + 5]
    anyway this is child’s play allow me,
    A man walked in to a bar , asking for something, the bartender imminently pulls out a gun and points it at the man face, the man pauses in shock, then says “thank you” and walks away. What was it that the man wanted?

  14. There is no point of adding $20 in $270.All of them actually paid $250 and the clerk took $20 for himself.This makes $270 and then we add discount in it of $30 and hence we get

    $250 + $20 + $30 = $300

    This question is nothing but ambiguous backward calculation which doesn’t makes sense at all.

  15. we will not count the 20 because it had already gone from the men’ pocket three men spend 270 and get a concession of 30

  16. @Sulaiman, the man asked to cure him of hiccups. when he asked the bartender he pulled out a gun therefor scaring the man and curing him… am i right???

  17. This simply involves the “reverse counting method”. In simple words this is just like the example of counting fingers of 1st hand in reverse order i.e (ten, nine, eight, seven and six) then adding the 5 fingers of the second hand and stating that these add upto 11 fingers.
    Similarly the $20 were already added to the clerk’s $250 that makes $270.

  18. This question is logically flawed, and the flaw can only be traced by having been alert while studying the question. The simple mathematics lends that each of the persons gave Rs. 90 in total. Out of Rs. 90, Rs. 83.334 would be given to Hotel and Rs, 6.667 would be given to Clerk. Hence, the clerk gets 6.667+6.667+6.667= Rs. 20 and the Hotel gets 83.334+83.334+83.334= Rs. 250. Therefore, in total both the Hotel & the Clerk get Rs. 20+ Rs. 250 = Rs. 270. And each of the person gets back Rs. 10 which reduces total bill (Clerk + Hotel) from Rs. 300 to Rs. 270.

  19. In the end when it is written that each man pays 90, and total comes to 270, that 270 also includes the clerks $20, as the eventual discount comes to 30 instead of 50, so there remains no question of the $10 remaining but $30, which are with the 3 men.

  20. You are double counting Clerk’s Tip …………………270$ is total expense including clerk’s tip…………….and 30$ return to 3 of them = 300$
    Puzzle solve……………….. Yahoooooooooooo……………..:)

  21. Each man took 10$ back in the end part. Right? “Each man” means that those three people plus the clerk, took 10$ back.So subtract 10$ of the clerk who took it back in that part.
    Solved. :)

  22. the amount of $270 already includes clerk’s tip $10, so no need to add this again.

    amount paid to hotel= { (total rent per man-discount given per man) + tip given by single man }* no.of total men
    ={ (100-16.67)+(20/3) }*3
    =269.99
    amount paid to hotel=270

  23. As all three men paid 250$ and 30$ which hotelkeeper gave back to three men.
    250$+30$=280$ and 20$ of manager equal to 300$.

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