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Mathematics ACE

Number Magic!Class: 1A4

Members: Chew Zhen Yuan 1A404

Keefe Ng WS 1A410

Number Trick?

S A pattern where:

can be applied for a range of results

results would be expected

Number Trick time!

S List down 3 consecutive positive integers between 1 and

100 inclusive!

(eg 45, 46 and 47)

S Take the product of the 3 numbers!

(45 x 46 x 47 =97290)

S Add 5 to the product!

(97290 + 5 = 97295)

Number Trick time! (continued)

S Multiply the result by 10!

(97295 x 10 = 972950)

S Add another 7 to the product!

(972950 + 7 = 972957)

S Multiply the sum again by 8!

(972957 x 8 = 7783656)

Number Trick time! (continued)

S Take away 456 from the preceding result!

(7783656 – 456 = 7783200)

S Divide the result by 40!

(7783200 ÷ 40 = 194580)

S Divide it again by the 2nd consecutive number that you have chosen!

(194580 ÷ 46 = 4230)

Number Trick time! (continued)

S Divide the product yet again by 2!

(4230 ÷ 2 = 2115)

S Add 1 to the result!

(2115 + 1 = 2116)

S Square root the sum for the final result!

√2116 = ……

46!!!!

Number Trick time! (continued)

S No matter which number you try, the result will always be

the 2nd consecutive number you have chosen!

S Go on, try it with the integers!

Reasoning

S Let’s take the middle integer (consecutive number) as n,

shall we?

S So, the numbers are:

n-1, n, n+1

S If you multiply the products, it will be:

(n-1)(n)(n+1)=n3-n

Reasoning (continued)

S If you add 5 to the product…

n 3-n+5

S Multiplying it by 10..

10(n3 – n + 5)= 10n3_10n+50

S After adding 7 to the product…

10n3_10n+50+7 = 10n3_10n+57

Reasoning (continued)

S Multiply the sum by 8:

8(10n3_10n+57) = 80n3-80n+456

S Taking away 456 from the product…

80n3-80n+456-456 =80n3-80n

S Dividing it by 40..

(80n3-80n)÷ 40 = 2n3-2n

Reasoning (continued)

S Now, divide it by the second consecutive number..

(2n3-2n) ÷ n = 2n2-2

S Divide it by 2!

(2n2-2) ÷ 2 = n2-1

S Add 1 to the result…

n2-1+1 = n2

Reasoning (continued)

S Lastly, square root the sum!

√n2= n (the 2nd consecutive number!!)

S Do you see the magic now? If you don’t, go back and

analyze the steps. Maybe you went wrong somewhere?

Question!

Qns: Can zero be included?

Ans: No

Exp: 0 is a neutral integer. If it is included, the product of the

three numbers would be regarded as the product of two. As

a result, if the integers are taken as 0, 1 and 2, the final

answer will be the square root of 3, which is 1.732050808….

Wrong!!

Oh wait!!!!

S Didn’t like the presentation??

S Here’s a potato