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nick1816
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In the number pyramid shown, where all numbers are positive integers, 24 Dec 2019, 05:21
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95% (hard)

Question Stats:

35% (02:37) correct 65% (02:02) wrong based on 65 sessions

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In the number pyramid shown, where all numbers are positive integers, each number is the sum of the two numbers below it {eg. a=b+c; b= d+e}. What is the maximum number of odd integers that can be in the pyramid?

A. 4
B. 5
C. 6
D. 7
E. 8
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D

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In the number pyramid shown, where all numbers are positive integers, 24 Dec 2019, 05:58
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nick1816
In the number pyramid shown, where all numbers are positive integers, each number is the sum of the two numbers below it {eg. a=b+c; b= d+e}. What is the maximum number of odd integers that can be in the pyramid?

A. 4
B. 5
C. 6
D. 7
E. 8
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Possible arrangement for maximum odd integers

-- -- -- -- -- -- O -- -- -- -- ---
-- -- -- -- -- E -- -- O -- -- -- --
-- -- -- - O -- --O -- -- E -- -- -
-- -- O -- -- E -- -- O -- -- O -- -

--> Total odd integers = 7

IMO Option D
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In the number pyramid shown, where all numbers are positive integers, 07 Jan 2020, 03:15
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nick1816
In the number pyramid shown, where all numbers are positive integers, each number is the sum of the two numbers below it {eg. a=b+c; b= d+e}. What is the maximum number of odd integers that can be in the pyramid?

A. 4
B. 5
C. 6
D. 7
E. 8
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Can anyone explain this ?
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In the number pyramid shown, where all numbers are positive integers, 07 Jan 2020, 04:07
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allkagupta

1. odd = even+odd

2. even= odd+odd

or

even= even+even

Because you have to maximize the number of odd numbers in the pyramid, split any even number in 2 odd numbers


Now there are 2 cases possible

1. a=even

.........E.........
.....O.......O....
..O......E........O
E....O.......O.......E

There are 6 odd numbers possible

2. a= odd

...........O.............
.......E........O.......
....O......O..........E
O......E.........O.........O

There are 7 odd numbers possible in this case
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In the number pyramid shown, where all numbers are positive integers, 20 Jan 2026, 05:01
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