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(#M40024811) SELF question Keep an EYE

find no. of 3 digit integers whose sum of digits is 16

Arneet Singh (10 years ago)

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Aishwarya Srikanth  (10 years ago)

Totally there are 72 three digit numbers which gives sum as 16.
Think logically. 1+6=7 so see the three digit nos which gives sum as 7.
start from 106=1+0+6=7 but not 16
next 115=1+1+5=7, likewise we get 7 but not 16 till 160
now see to 169=1+6+9=7+9=16
178=8+8=16
187=1+8+7=16
196=1+9+6=16. So there are 4nos between 100 and 200 which gives sum as 16.
Likewise from 200 to 300, we have 5nos 259,268,277,286,295
From 300 to 400, we have 6nos 349,358,367,376,385,394
From 400 to 500, we have 7nos 439,448,457,466,475,484,493
From 500 to 600, we have 8nos 529,538,547,556,565,574,583,592
From 600 to 700, we have 9n0s 619,628,637,646,655,664,673,682,691
From 700 t0 800, we have 11nos 709,718,727,736,745,754,763,772,781,790,799
From 800 to 900, we have 11nos 808,817,826,835,844,853,862,871,880,889,898
From 900 to 999, we have 11nos 907,916,925,934,943,952,961,970,979,988,997
Totl nos=4+5+6+7+8+9+11+11+11=72
Solutio : 72.

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anshu  (10 years ago)

ans is
111

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Arneet Singh  (10 years ago)

please explain how did you solved it?

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