Luigi from Humanitree and Karrthic from Australian International School Malaysia found an algebraic expression for the final number. This is Karrthic's work: The operation is $(x +4) \times 2 -7= y$ For example $(5 + 4) = 9\\ 9 \times2 = 18\\ 18-7=11$ When you reverse the operation, you find $x$Furkan from TED Ankara Koleji in Turkey, Bernd and Qianwei from Humanitree and Shriya from International School Frankfurt in Germany showed what the computer does algebraically. This is Qianwei's work: $(x+4) \times 2 - 7=y$ If we want to get $x$, we need to do the opposite of this equation. Start with $y.$ In the equation $7$ [was subtracted], so we need to add $7$ to $y$ $(7+y)$ In the equation, $(x+4)$ was doubled, we need to divide it by two to get the opposite. $(7+y)\div2$ In the equation, $x$ was added [to] $4$, to get the opposite, we need to take away $4$ from $x.$ $(y+7)\div2-4$ Finally the equation we used to find $x$ will be: $(y+7)\div2-4=x$Furkan and Shriya simplified the equation before 'reversing' it. This is Furkan's work: $(x+4) \times2 - 7$ is equal to $2x + 1,$ so we subtract $1$ from the result and divide by $2$ to get the starting number.Alex from Humanitree and Fernando from Academia Britanica Cuscatleca in El Salvador noticed a different pattern in the numbers from the computer. This is Fernando's work: When following the instructions given in the problem, if [you give the computer random integers as the result of your calculation], you will get random numbers. However, when we start with 1 and try until five, you will notice the sequence:
The answer to the subsitution is always 0.5 greater than the actual answer, therefore, we need to always substract 0.5 Therefore, the instructions are directly 0.5$n-$0.5 ! Can you see how this result is related to Furkan's equation?
We received lots of sets of instructions for similar activities. Federico from Humanitree used algebra: Subtract 10 Divide by 4 Add 5 If the number was $n$ You would do $(n-5) \times4 +10 = $ end number ($x$) Then the computer would do this operation to get the original value of $n:$ $(x-10)\div4 +5 =$ starting number This operation would give you the original results.Abdullah from Poland wrote a Python program to guess your number: print("YOUR NUMBER WAS...") print() print("Press [ENTER] after you made each move.") print() input("Think of a number.") print() input("Add 9") print() input("Divide it by 4") print() input("Subtract 6") print() input("Triple it") print() input("Subtract 23") number = float(input("Now, type in number you finished with and then press enter.")) print("Processing...") answer = (((number + 23) / 3) + 6) * 4 - 9 print("You chose the number %s" % answer)
Leila C and Scarlett K from Westridge School for Girls and KSc from Cheadle Academy sent in interesting sets of instructions which will always give the same result, like in the problem Your Number Is... If you follow these instructions, will it ever be possible for the computer to work out what number you started from? These are KSc's instructions:
Tejas V K.
A student has been asked to multiply a given number by 8/17 instead he divides the given number by 8/7.His answer is 225 more than the correct answer.What is the given number? 1 Expert AnswerThe Staff Selection Commission has released the exam date for Paper I of the SSC CPO 2022 exam. As per the notice, Paper I of the SSC CPO is scheduled to be held from 9th November to 11th November 2022. A total number of 4300 candidates will be appearing for the SSC CPO 2022 exam. The Staff Selection Commission (SSC) is soon going to release the admit card for the SSC CPO Paper I exam. To crack the exam, candidates should follow a proper SSC CPO Study Plan. The candidates who will clear the exam will get a salary range between Rs. 29,200/- to Rs. 11,2400/- |