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Riddle (simple arithmetic problem/illusion)

I have this small story (sorry about my bad English) : One man (M) took 25 dollar from man (A), and another 25 dollar from man (B), so now man (M) has 50 dollar. Man (M) spent 45 dollar from the 50 he had. The reminder he has now is 5 dollar. He used this reminder to give man(A) 1 dollar, and also give man(B) 1 dollar. That means as though that man (A) gave man(M) 24 dollar from the beginning, the same is for man(B), it seems he gave man(M) 24 dollar. Now man (M) has 3 dollar. Now, if we calculate the total: 24 + 24 + 3 =51, so we have 1 more dollar! From where it came? ?

And how can I show the trick by mathematical equations ?


marked as duplicate by J. M. is a poor mathematician, user940, Henning Makholm, Zev Chonoles Jan 3 '12 at 16:23

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  • $\begingroup$ Same problem as in this question. Shall we close this as a duplicate? $\endgroup$ – Zev Chonoles Jan 3 '12 at 16:10
  • $\begingroup$ @Zev Chonoles: I am asking here about showing it by equations .. not the same question. $\endgroup$ – Adban Jan 3 '12 at 16:12
  • 2
    $\begingroup$ It is really the same problem, you're just not seeing it. For the sake of the question, here's why you get that weird $51$ ; you're not adding the right things.. if you compute the total, man $M$ took $24$ from man $A$ and man $B$, and he has spent $45$ dollars over his things, so he's left with $3$ dollars, fine. But the total would be $1+1+3 + 45 = 50$, which has nothing to do with $24+24+3$. (One dollar in A/B's pockets, $3$ in M's pockets and 45 dollars in candy.) $\endgroup$ – Patrick Da Silva Jan 3 '12 at 16:17

Well, the trick is of words, while he in fact still has 3 dollars, the debt he has is of 48.

$(25 + 25) - 2 = 48$

He has spent 45 dollars so far so

$48 - 45 = 3$

He still has 3 dollars.


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