Find a given number using two given numbers

Someone posted this on a site I frequent, and I can't figure it out either.

Quote:

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Ok guys, I've been racking my brain for quite a while trying to figure this out. Basically we have two numbers we can use, and we need to use those two numbers to create a formula for finding the third number. You can use the numbers as many times as you want, but you can only use the numbers provided as long as you find a trustworthy formula. I'll provide two sets of numbers for you to test your formula on.

Set #1:
using these two numbers:
36926104
33360
find this number:
14616

Set #2
using these two numbers:
38221976
44040
find this number:
25084

To anyone who participates, thankyou so much for your help.

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Quote:

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Originally Posted by Tural

Someone posted this on a site I frequent, and I can't figure it out either.

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...and the formula involves what? Just + - * / or some more sophisticated functions? Can you use each number only once?

It sounds like , Given 2 Numbers, you must divise a formula only using those two numbers in any mathematical combinatorial formula, any number of times, ie...

If A = 2 and B = 3 and C = 116 then
(2 + 3)³ - 3² = C

So I have a solution to the first one:

Quote:

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If A = 36926104
And B = 33360

Then Lets say C = A mod B
D = B mod C
E = C Mod D

and so on:


We get:

A = 36926104
B = 33360
C = 29944 (A Mod B)
D = 3416 [B Mod (A Mod B)]
E = 2616 [(A Mod B) Mod [B Mod (A Mod B)]]
F = 800 <[B Mod (A Mod B)] Mod [(A Mod B) Mod [B Mod (A Mod B)]]>
G = 216 {[(A Mod B) Mod [B Mod (A Mod B)]] mod <[B Mod (A Mod B)] Mod [(A Mod B) Mod [B Mod (A Mod B)]]>}
H = 152 |<[B Mod (A Mod B)] Mod [(A Mod B) Mod [B Mod (A Mod B)]]> MOD {[(A Mod B) Mod [B Mod (A Mod B)]] mod <[B Mod (A Mod B)] Mod [(A Mod B) Mod [B Mod (A Mod B)]]>}|


Now, Lets say W = C-D-D-D-D-D
Or:

W=(A Mod B)-[B Mod (A Mod B)]-[B Mod (A Mod B)]-[B Mod (A Mod B)]-[B Mod (A Mod B)]-[B Mod (A Mod B)]

Next Lets say X = W+F+F
Or:
X=(A Mod B)-[B Mod (A Mod B)]-[B Mod (A Mod B)]-[B Mod (A Mod B)]-[B Mod (A Mod B)]-[B Mod (A Mod B)]+<[B Mod (A Mod B)] Mod [(A Mod B) Mod [B Mod (A Mod B)]]>+<[B Mod (A Mod B)] Mod [(A Mod B) Mod [B Mod (A Mod B)]]>

And Finally, lets say Y=X+H
Or
Y=(A Mod B)-[B Mod (A Mod B)]-[B Mod (A Mod B)]-[B Mod (A Mod B)]-[B Mod (A Mod B)]-[B Mod (A Mod B)]+<[B Mod (A Mod B)] Mod [(A Mod B) Mod [B Mod (A Mod B)]]>+<[B Mod (A Mod B)] Mod [(A Mod B) Mod [B Mod (A Mod B)]]>+|<[B Mod (A Mod B)] Mod [(A Mod B) Mod [B Mod (A Mod B)]]> MOD {[(A Mod B) Mod [B Mod (A Mod B)]] mod <[B Mod (A Mod B)] Mod [(A Mod B) Mod [B Mod (A Mod B)]]>}|


We end up with Y=14616

Or:

14616=(36926104 Mod 33360)-[33360 Mod (36926104 Mod 33360)]-[33360 Mod (36926104 Mod 33360)]-[33360 Mod (36926104 Mod 33360)]-[33360 Mod (36926104 Mod 33360)]-[33360 Mod (36926104 Mod 33360)]+<[33360 Mod (36926104 Mod 33360)] Mod [(36926104 Mod 33360) Mod [33360 Mod (36926104 Mod 33360)]]>+<[33360 Mod (36926104 Mod 33360)] Mod [(36926104 Mod 33360) Mod [33360 Mod (36926104 Mod 33360)]]>+|<[33360 Mod (36926104 Mod 33360)] Mod [(36926104 Mod 33360) Mod [33360 Mod (36926104 Mod 33360)]]> MOD {[(36926104 Mod 33360) Mod [33360 Mod (36926104 Mod 33360)]] mod <[33360 Mod (36926104 Mod 33360)] Mod [(36926104 Mod 33360) Mod [33360 Mod (36926104 Mod 33360)]]>}|

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