@abakcus Lets complicate thing for this boy who seems to know it is 2

@abakcus @mdrechsler 2

@abakcus (10²+11²+12²+13²+14²)/365 = (100+121+144+169+196)/365 = (221 + 313 + 196)/365 = 730/365 = 2

@abakcus that young man knows the answer is two

@abakcus the answer is 2

@abakcus 3²+4²=5² 10²+11²+12²=13²+14² 21²+22²+23²+24²=25²+26²+27² 4 12 24 40 60 1.2.2 2.2.3 2.3.4 2.4.5 2n(n+1) (2n(n+1)-n)²+(2n(n+1)-n+1)²...(2n(n+1))²=(2n(n+1)+1)²+...(2n(n+1)+n)² n=10 => 210²+211²+....+220²=221²+...+230²

@abakcus If you are expected to assume the answer is an integer, then it isn’t hard at all

@abakcus Que belleza de pintura 😌

@abakcus Helpful method: Know your square numbers, otherwise foil: (e.g 13×13 = (10+3)(10+3) = 100+30+30+9). Sum last digits: 6+9+4+1 = (9+1)+(6+4) = 0 (carry 2) Sum next digits: 2+4+6+9 = (9+2)+(6+4)+2 = 3 (carry 2) Sum next digits: 5×1+2 = 7 Digit readout: 730 365×2=730 ∴ 730/365 = 2

@abakcus What a scene

@abakcus @mathladyhazel Great 🖼 Numerator equals 730=500+200+30=5·10²+2·10·(1+2+3+4)+(1²+2²+3²+4²), -having observed that 14=10+4, 13=10+3, etc-. 😊

@abakcus I was never good at Cossack math.

@abakcus (10²+11²+12²+13²+14²)/365 = (10²+11²+12²)/365 + (13²+14²)/365 = 1 + 1

@abakcus 2

@abakcus 10^2+11^2+12^2=100+121+144=365 13^2+14^2=169+196=365 So the answer is (365+365)/365=2.

@abakcus @mathladyhazel The answer is 2, and yes, done as mental arithmetic. It's actually quite cute. Happy to say I can still do it. Can't do countdown fast enough though.

@abakcus 2

@abakcus 100+4*10^2+1+4+9+16+2(10+20+30+40)=730/2=365

@abakcus I did 10^2 = 100 11^2= a 1 then unit+unit then unit*unit so 121 12^2 = 1 then 2+2 then 2*2 13^2 … 14.. 10 + 11 + 12 each squared was 365 locked that then added the last two together

@abakcus Sum of 1 to n^2= n(n+1)(2n+1)/6 Sum of 1 to 14^2= 14*15*29/6 Sum of 1 to 9^2= 9*10*19/6 Subtract sums to get 730 and divide by 365 =2